# WORKSHEET ON SPEED DISTANCE AND TIME 2

Problem 1 :

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?

Problem 2 :

Two trains are running at 40 kmph and 20 kmph respectively in the same direction .Faster train completely passes a man who is sitting in the slower train in 9 seconds. What is the length of the faster train ?

Problem 3 :

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. Find the ratio of their speeds.

Problem 4 :

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?

Problem 5 :

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find the time taken by the two trains to cross each other. Problem 1 :

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?

Solution :

Let the trains meet each other "m" hours after 7 a.m.

Distance covered by the train from A in "m" hrs is

=  Speed  Time

=  20 kms

At a particular time after 8 a.m, if the train from A had traveled "m" hours, then the train from B would have traveled (m-1) hours.

Because it started at 8.00 am. (one hour later)

Distance covered by the train from B in (m - 1) hrs  is

=  25(m - 1)

At the meeting point,

sum of the distances covered by the two trains is equal to the total distance (from A to B).

That is

20m + 25(m-1)  =  110

20m + 25m - 25  =  110

45m  =  135

m  =  3 hours

So, two trains meet each other 3 hrs after 7 a.m

That is, at 10 a.m.

So, the time at which they will meet is 10 a.m.

Problem 2 :

Two trains are running at 40 kmph and 20 kmph respectively in the same direction .Faster train completely passes a man who is sitting in the slower train in 9 seconds. What is the length of the faster train ?

Solution :

Relative speed of two trains is

=  40 - 20

=  20 kmph

=  20  5/18 m/sec

=  50/9 m/sec

Given : Faster train completely passes a man who is sitting in the slower train in 9 seconds.

Length of the faster train is

=  The distance covered by the faster train in this 9 seconds

=  Speed  Time

=  50/9  9

=  50 m

So, the length of the faster train is 50 m.

Problem 3 :

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. Find the ratio of their speeds.

Solution :

Let "a" m/sec and "b" m/sec be the speeds of two trains respectively

First train crosses the man in 27 seconds with speed "a" m/sec

So, the length of the first train is

=  Distance covered in 27 seconds

=  Speed ⋅ Time

=  a ⋅ 27

=  27a -----(1)

Second train crosses the man in 17 seconds with speed "b" m/sec

Length of the second train is

=  Distance covered in 17 seconds

=  Speed ⋅ Time

=  b ⋅ 17

=  17b -----(2)

Given : The given two trains cross each other in 23 seconds.

The distance covered by the two trains in this 23 seconds is

=  Sum of the lengths of the two trains

=  Relative speed  Time

=  (a + b)  23

=  23a + 23b -----(3)

We know the fact that when two trains cross each other in opposite directions, the distance covered by them is equal to sum of the length of the two trains.

That is,

(1) + (2)  =  (3)

27a + 17b  =  23a + 23b

4a  =  6b

a / b  =  6 / 4

a / b  =  3 / 2

a : b  =  3 : 2

So, the ratio of their speeds is 3:2.

Problem 4 :

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?

Solution :

Speed of the train  =  54 kmph

=  54  5/18 m/sec

=  15 m/sec

The train passes the man in 20 seconds.

The distance covered by the train in this 20 seconds is equal to the length of the train.

Distance  =  Speed ⋅ Time

Distance  =  20 ⋅ 15

Distance  =  300 m

So, length of the train is 300 m.

Let "m" be the length of the platform

Given : The train crosses the  platform in 36 seconds.

We know the fact that the distance covered by the train in this 36 seconds is equal to sum of the lengths of the train and platform

Then, the distance covered by the train in 36 seconds is

=  300 + m

So, the train takes 36 seconds to cover the distance "300 + m"

Time  =  Distance / Speed

36  =  (300 + m) / 15

540  =  300 + m

240  =  m

So, the length of the platform is 240 meters.

Problem 5 :

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find the time taken by the two trains to cross each other.

Solution :

Relative speed  is

=  60 + 90  =  150 kmphr

=  150  5/18 m/sec

=  125/3 m/sec

When they cross each other, distance covered by both the trains  is equal to sum of the lengths of the two trains.

So, the distance covered by them is

=  1.1 + 0.9

=  2 km

=  2  1000 m

=  2000 m

Time taken by the two trains to cross each other is

=  Distance / Speed

=  2000 / (125/3)

=  2000  3/125

=  48 seconds

So, time taken by the two trains to cross each other is 48 seconds. Apart from the problems given above, if you need more problems on speed, distance and time, please click the following links.

Worksheet on Speed, Distance and Time

Worksheet on Speed, Distance and Time - 3

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

1. Click on the HTML link code below.

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 