Wednesday, February 1, 2023

How To Solve Two Trains Math Problem

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A Less Obvious But More Productive Way To Represent The Problem:

Speed distance math problem trains in opposite direction – Concepts and Tricks

    How much time does the bird spend in flight? If you representthe problem in terms of the amount of time the bird is flying, then a solutionis fairly straightforward. The two trains are 50 miles apart, and are approachingeach other at a relative speed of 50 mph , so it will take onehour for them to meet. If the bird spends one hour flying at 100 mph, thenit will traverse 100 miles before the trains meet.

More Solved Examples On Speed Distance And Time

Example 1. A boy travelled by train which moved at the speed of 30 mph. He then boarded a bus which moved at the speed of 40 mph and reached his destination. The entire distance covered was 100 miles and the entire duration of the journey was 3 hours. Find the distance he travelled by bus.


Let the time taken by the train be t. Then that of bus is 3-t.

The entire distance covered was 100 miles

So, 30t + 40 = 100

Solving which gives t=2.

Substituting the value of t in 40, we get the distance travelled by bus is 40 miles.

Alternatively, we can add the time and equate it to 3 hours, which directly gives the distance.

d/30 + /40 = 3

Solving which gives d = 60, which is the distance travelled by train. 100-60 = 40 miles is the distance travelled by bus. Example 2. A plane covered a distance of 630 miles in 6 hours. For the first part of the trip, the average speed was 100 mph and for the second part of the trip, the average speed was 110 mph. what is the time it flew at each speed?


Our table looks like this.


Assuming the distance covered in the 1st part of journey to be d, the distance covered in the second half becomes 630-d.

Assuming the time taken for the first part of the journey to be t, the time taken for the second half becomes 6-t.

From the first equation, d=100t

The second equation is 630-d = 110.

Substituting the value of d from the first equation, we get

630-100t = 110

Solving this gives t=3.



d/3 = /4

Problem 1:

Motion In The Same Direction : The Basics

All types of motion questions on the GMAT require you to apply the following basic Distance Formula:

Distance = Rate * Time

The general idea with Same Direction or Catch Up motion questions is that you have two entities moving in the same direction at different rates of speed. One entity usually starts after the other entity and travels at a faster rate of speed to catch up with the first entity. The question itself will generally ask you to figure out how long it takes for the second entity to catch up with the first entity, or perhaps how much distance the second entity must travel before overtaking the first entity.

Regardless of what information is given to you and what youre ultimately asked to solve for, these questions always come down to solving for one of the variables in the Distance Formula. There are three crucial steps to finding the missing piece that the question is asking you to solve for.

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The Bad Rep Of Word Problems: Two Trains Leave The Station

by Susan Jo Russell | Oct 22, 2018 |

When people want to make a joke about how difficult, convoluted, or inaccessible word problems are, they often cite some version of the two trains problem. You can see an example of this problem here:

Maybe you want to try solving this problem yourself before reading on.

The two trains problem has become an emblem in popular culture. Saying the opening phrase, Two trains leave different stations at the same time , invariably results in uncomfortable laughter. It surfaces memories of school problems that seemed convoluted and inaccessible and the inadequacy many people felt when faced with them.

The belief that what we used to call word problems, and now more often refer to as story problems, are more difficult than straightforward calculation also pervades teaching at the elementary grades. Teachers we work with often say, for example, that they teach calculation first, only later moving to what they think of as the more difficult challenge of story problems. Story problems are seen as a separate piece of instruction. What if, instead, we think of the idea of story as integral to learning about the operations from the beginning?

Before you continue reading, pause and think through Fionas thinking. What parts of the problem has she solved? What does she need to do to finish the problem?

Speed And Distance Problems

The Train Fly Problem

Have you ever heard of a word problem like this one? “Train A heads north at an average speed of 95 miles per hour, leaving its station at the precise moment as another train, Train B, departs a different station, heading south at an average speed of 110 miles per hour. If these trains are inadvertently placed on the same track and start exactly 1,300 miles apart, how long until they collide?”

If that problem sounds familiar, it’s probably because you watch a lot of television . Whenever TV shows talk about math, it’s usually in the context of a main character trying but failing miserably to solve the classic “impossible train problem.” I have no idea why that is, but time and time again, this problem is singled out as the reason people hate math so much.

Kelley’s Cautions

Make sure that the units match in a travel problem. For instance, if the problem says you traveled at 70 miles per hour for 15 minutes, then r = 70 and t = 0.25. Since the speed is given in miles per hour, the time should be in hours also, and 15 minutes is equal to .25 hours. I got that decimal by dividing 15 minutes by the number of minutes in an hour: 1560 = 14 = 0.25.

In fact, it’s not so hard. This, like any distance and rate of travel problem, only requires one simple formula:

  • D = r t
Critical Point
DA = 95t DB = 110t
Kelley’s Cautions
You’ve Got Problems
  • DA + DB = 1300

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Problems On Trains With Solutions

Problem 1 :

If the speed of a train is 20 m/sec, find the speed the train in kmph.

Solution :

Speed = 20 x 18/5 m/sec

Speed = 72 kmph

Hence, the speed of the train is 72 kmph.

Problem 2 :

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.

Solution :

Distances needs to be covered to cross the platform is

= Sum of the lengths of the train and platform

So, distance traveled to cross the platform is

= 300 + 500

Time taken to cross the platform is

= Distance / Speed

Hence, time taken by the train to cross the platform is 40 seconds.

Problem 3 :

A train is running at a speed of 20 m/sec.. If it crosses a pole in 30 seconds, find the length of the train in meters.

Solution :

The distance covered by the train to cross the pole is

= Length of the train

Given : Speed is 20 m/sec and time taken to cross the pole is 30 seconds

We know,

length of the train = Speed Time

Length of the train = 20 30

Length of the train = 600 meters

Hence, length of the train is 600 meters.

Problem 4 :

It takes 20 seconds for a train running at 54 kmph to cross a platform.And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 kmph in the same direction in which the train is running. What is the length of the train and length of platform .

Solution :

Relative speed of the train to man = 54 – 6 = 48 kmph

= 48 5/18 m/sec

= 40/3 m/sec

= 12

Use Problem Breakdown And Change Analysis Techniques To Solve The Problems In A Few Simple Steps

The problems involving Time and Distance are taught during middle schools and also form an important part of most of the competitive job tests such as SSC CGL, Bank POs etc. In this second session of solving difficult SSC CGL level Time and Distance problems in a few steps, we will solve two chosen problems and analyze the elegant solution process in a few steps.

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Two Trains Passes In The Same Direction

Here we will learn about the concept of two trains passes inthe same direction.

When two train passes a moving object inthe same direction.

Let length of faster train be lmeters and length of slower train be m meters

Speed of faster train be x km/hr and speed of slower trainbe y km/hr

Relative speed = km/hr

Then, time taken by the faster train to pass the slowertrain = meters/ km/hr

Note: Change km/hr to m/sec

Now we will learn to calculate when two trains running onparallel tracks in the same direction.

Solved examples when twotrains passes in the same direction:

1. Two trains 130m and 140 m long are running on parallel tracks in the same direction with a speedof 68 km/hr and 50 km/hr. How long will it take to clear off each other fromthe moment they meet?


Example: Alex Puts $2000 In The Bank At An Annual Compound Interestof 11% How Much Will It Be Worth In 3 Years

Two Trains Leaving a Station – Rate System of Equations Word Problem (Example)

This is the compound interest formula:

So we will use these letters:

  • Present Value PV = $2,000

Note: we could have also tried “guess and check”:

  • We could try, say, n=10: 10 = 120 NO
  • Next we could try n=12: 12 = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of ×.


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Types Of Questions On Train Problems

Over the years, the exam pattern has changed with the increase in the number of applicants and every year candidates notice a new pattern or format in which questions are asked for various topics in the syllabus.

It is important that a candidate is aware of the types in which a question may be framed or asked in the examination to avoid any risk of losing marks.

Thus, given below are the type of questions which may be asked from the train-based problems:

  • Time Taken by Train to Cross any stationary Body or Platform Question may be asked where the candidate has to calculate the time taken by a train to cross a stationary body like a pole or a standing man or a platform/ bridge
  • Time Taken by 2 trains to cross each other Another question that may be asked is the time two trains might take to cross each other
  • Train Problems based on Equations Two cases may be given in the question and the candidates will have to form equations based on the condition given
  • Aspirants must also refer to the important pointer given below for the Train problems.

    The image given below mentions the basic points a candidate must remember in order to answer the train based word problems:

    Turning English Into Algebra

    To turn the English into Algebra it helps to:

    • Read the whole thing first
    • Do a sketch if possible
    • Assign letters for the values
    • Find or work out formulas

    You should also write down what is actually being asked for, so you know where you are going and when you have arrived!

    Also look for key words:

    When you see

    $N = $12

    So Joels normal rate of pay is $12 per hour


    Joels normal rate of pay is $12 per hour, so his overtime rate is 1¼× $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

    More about Money, with these two examples involving Compound Interest

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    Where Can I Get Aptitude Problems On Trains Questions And Answers With Explanation

    IndiaBIX provides you lots of fully solved Aptitude questions and answers with Explanation. Solved examples with detailed answer description, explanation are given and it would be easy to understand. All students, freshers can download Aptitude Problems on Trains quiz questions with answers as PDF files and eBooks.

    Tips And Tricks To Solve Train Problems

    Pin by CreatingSuccess on Math

    To assist aspirants to prepare for and ace the quantitative aptitude section, given below are a few tips which may help you answer the train problems quicker and more efficiently:

    • Always read the question carefully and do not haste in answering it as the train-based questions are usually presented in a complex manner
    • Once you read the question, try to apply a formula in them, this will may solution direct and save you some time
    • Do not guess if you are not sure. Since there is negative marking in competitive exams, ensure that you do not make assumptions and answer the questions
    • Do not over complicate the question and spend too much time on solving it if you are not able to answer
    • In case of confusion, you can also refer to the options given in the objective type papers and try finding the answer with the help of options given

    Candidates can refer to the below-mentioned links and solve more and more mock tests, question papers and practise papers to apprehend the level of the exam better:

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    This Problem Has Been Solved


    The two trains problem is a classic algebra problem. In thislab, we will write a program in python to solve every version ofthis problem.

    This problem follows a basic pattern. The values will bereplaced by variables in the below question.

    Train A, traveling X miles per hour,leaves place1 headingtoward place2, total miles away. At the same timeTrain B, traveling Y mph, leaves place2 headingtoward place1. When do the two trains meet? How far are theyfrom each city?

    In this lab, you will write a problem that solves this problem.Then you will never have to do it by hand again.

    When the meet is determined by

    time in hours = /

    The distance from place1 is time*X.

    The distance from place2 is time*Y.

    You may assume that X, Y, and total will be integer values. Theresults should be given as decimal numbers rounded to 2 digits.

    The command round can be used to round.

    Your program should look like the below example. The solution tothe Dr. Math example is given below.

    Solve the Two Trains Problem.Enter First Speed: 70Enter First Place: WestfordEnter Second Speed: 60Enter Second Place: EastfordEnter total distance: 260Word ProblemTrain A, traveling 70 miles per hour, leaves Westford heading toward Eastford , 260 miles away. At the same time Train B, traveling 60 mph, leaves Eastford heading toward Westford . When do the two trains meet? How far are they from each city?AnswersThey meet after 2.0 hours.Train A is 140.0 miles from WestfordTrain B is 120.0 miles from Eastford

    Distance Problems: Traveling In Opposite Directions

    Example:A bus and a car leave the same place and traveled in opposite directions. If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart?

    Solution:Step 1: Set up a rtd table.


    Answer: They will be 210 miles apart in 2 hours.

    Example of a distance word problem with vehicles moving in opposite directions

    In this video, you will learn to solve introductory distance or motion word problems – for example, cars traveling in opposite directions, bikers traveling toward each other, or one plane overtaking another. You should first draw a diagram to represent the relationship between the distances involved in the problem, then set up a chart based on the formula rate times time = distance.

    The chart is then used to set up the equation.

    Example:Two cars leave from the same place at the same time and travel in opposite directions. One car travels at 55 mph and the other at 75 mph. After how many hours will they be 520 miles apart?

    Solve this word problem using uniform motion rt = d formula:

    Example:Two cyclists start at the same corner and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hours, they are 81 miles apart. Find the rate of each cyclist.

    Distance – Opposite Directions

    Example:Brian and Jennifer both leave the convention at the same time traveling in opposite directions. Brian drove at 35 mph and Jennifer drove at 50 mph. After how much time were they 340 miles apart?

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    When Will These Two Trains Meet Each Other

    I cant seem to solve this problem.

    A train leaves point A at 5 am and reaches point B at 9 am. Another train leaves point B at 7 am and reaches point A at 10:30 am.When will the two trains meet ? Ans 56 min

    Here is where i get stuck.I know that when the two trains meets the sum of their distances travelled will be equal to the total sum , here is what I know so far

    Time traveled from A to B by Train 1 = 4 hours

    Time traveled from B to A by Train 2 = 7/2 hours

    Now if S=Total distance from A To B and t is the time they meet each other then

    $$\text_}= S =\frac + \frac $$

    Now is there any way i could get the value of S so that i could use it here. ??

    • $\begingroup$I guess its 56 min after train B leaves the station. So its 7:56 Am$\endgroup$

    We do not need $S$.

    The speed of the train starting from $A$ is $S/4$ while the speed of the train starting from $B$ is $S/ = 2S/7$.

    Let the trains meet at time $t$ where $t$ is measured in measured in hours and is the time taken by the train from $B$ when the two trains meet. Note that when train $B$ is about to start train $A$ would have already covered half its distance i.e. a distance of $S/2$.

    Hence, the distance traveled by train $A$ when they meet is $\dfrac2 + \dfrac4$.

    The distance traveled by train $B$ when they meet is $\dfrac7$.

    Hence, we get that $$S = \dfrac2 + \dfrac + \dfrac$$ We can cancel the $S$ since $S$ is non-zero to get $$\dfrac12 = \dfrac4 + \dfrac7$$ Can you solve for $t$ now?

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