# HOW TO SOLVE TIME AND DISTANCE PROBLEMS

## About the topic "How to solve time and distance problems"

"How to solve time and distance problems" is a big question having had by the people who get prepared for competitive exams and study quantitative aptitude. Solving time and distance problems is  never being easy and always it is a challenging one for any student.

## How to solve time and distance problems?

The answer  for the question "How to solve time and distance problems" is purely depending upon the question that we have in the topic "Time and Distance Problems". The techniques and methods we apply to solve problems in time and distance  will vary from problem to problem.

The techniques and methods we apply to solve a particular  problem  will not work for another word problem in time and distance.

Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly involved in "How to solve time and distance problems"

## Points to remember

 1. Speed or Velocity = Distance / Time 2. Distance= Speed x Time 3. Time = Distance / Speed 4. a km/hr= (ax5/18) m/sec 5. b m/sec = (bx18/5) km/hr. 6. If the ratio of the speeds of A and B is a:b, then ratio of time taken by them to cover the same distance is b:a 7. If a certain distance is covered at p km/hr and an equal distance is covered at q km/hr, then the average speed of the whole journey is = (2pq)/(p+q) km/hr

To get answer for the question "How to solve time and distance problems? ", let us look at the steps involved in solving the problem given below in time and distance.

Problem:

A person covers a certain distance at a certain speed. If he increases his speed by 33 1/3%, he takes 15 minutes less to cover the same distance. Find the time taken by him initially to cover the distance at the original speed.

Solution:

Step 1 :

Let us understand the given information. There are two information given in the question.

1. A person covers a certain distance at a certain speed.

2. If the speed is increased by 33 1/3 %, he takes 15 minutes less to cover the same distance.

Step 2 :

Target of the question: Time taken by him initially to cover the distance at the original speed.

Step 3 :

Let 100% be the original speed.

If the speed is increased by 33 1/3%, then the speed after increment is 133 1/3%.

Step 4 :

Ratio of the speeds  = (100 %) : (133 1/3%)

= 100 : 400/3

Ratio of the speeds   = 1 : 4/3

Step 5 :

If the ratio of the speeds is  1:4/3,

the ratio of time taken would be 1:3/4

Step 6 :

When the speed is increased by 33 1/3%, 3/4 of the original time is enough to cover the same distance.

That is,when the speed is increased by 33 1/3%, 1/4 of the original time will be decreased -------(1)

The question says that when speed is increased by 33 1/3%, time is decreased by 15 minutes -------(2)

Let "x" be the original time.

Comparing the statements (1) & (2), we get

1/4 of "x"  = 15 minutes

(1/4)x = 15 minutes

x = 15x4

x = 60

Original time = 60 minutes

Hence, time taken by him initially = 60 minutes or 1 hour

We hope, you would have received answer for the question "How to solve time and distance problems?" after having seen the steps involved in solving the above problem in time and work . Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic