 # Distance – Definition, Formula, Examples | How to find the Distance when Speed and Time are given?

Do you have any difficulties in solving the problems related to distance, average distance, the distance between two points, etc? Then, look no further and make use of our article on how to find distance when speed and time are given. We have covered everything such as distance definition, units, formula, procedure on how to find distance along with examples. Refer to the problems on calculating distance here and get an idea on how to approach to solve similar kinds of distance problems in your homework or assignments easily.

### Distance – Definition

Distance is defined as the complete path traveled by the object. You can better understand this statement with an example. Let suppose a car travels in the direction of north 8th km and then moves towards east 5 km. here the total distance traveled by car is 13 km as it is a complete path.

### Distance Formula

The formula used to determine the distance when speed and time are known is distance = speed*time.  Units for distance are m, km, miles, etc.

### How to Calculate Distance?

Follow the simple steps listed below to find distance easily and they are along the lines

• Initially, find what’s known from the given information such as speed, time.
• Check whether both the metrics are given are in the same unit of measurement. If not convert accordingly to the same units.
• Later, substitute the known values speed, time in the formula for distance = speed*time
• Simplify further and find the total distance traveled by the object.

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### Problems on Calculating Distance

Example 1.
Cyclists travel at a speed of 15 km/hr. At what distance would they travel in 80 minutes?
Solution:
Cyclists travel with the speed=15 km/hour
time=80 minutes=80/60 hours
We have to find the distance
distance=speed × time
=15 × 80/60
=20
Therefore, the cyclists would travel a distance of 20 km.

Example 2.
A boy walking at a speed of 5 km/hr reaches his school 10 min late. The next day at a speed of 10 km/hr reaches his school 5 minutes late. Find the distance of his school from his house?
Solution:
Given,
A boy walking at a speed of 5 km/hr reaches his school late by=10 min
The next day boy walks at a speed of 10 km/hr reaches his school late by=5 minutes
Difference between time=10-5=5 min=5/60=1/12 hr
The distance of his school from his house=10 × 5/10-5 × 1/12
=50/5 × 1/12
=10/12
=5/6 =0.833 km

Example 3.
Radha and Sudha are standing at two ends of a room with a width of 60 m. They start walking towards each other along the width of the room with a Speed of 4 m/s and 1 m/s, respectively. Find the total distance traveled by Radha when he meets Sudha for the third time?
Solution:
When Radha meets Sudha for the third time, they together would have covered the distance of 5d, i.e. 5 × 60 m=300 m
The ratio of speeds of Radha and Sudha =4:1
The total distance traveled by them will also be in the ratio 4:1  as the time taken is constant.
So the distance traveled by Radha will be 4/5 × 300=240 m

Example 4.
Mani drives his car at a speed of 80 km per hour. How much distance will he cover in 3 hours 30 minutes?
Solution:
Mani drives his car at a speed=80 km
Time taken=3 hours 30 minutes
=3 1/2 hours
Distance covered in 1 hour=80 km
Distance covered in 3 hours 30 minutes=80 × 3 1/2 km
=80 × 7/2 km
=280 km
Hence, Mani covers a distance of 280 km.

Example 5.
A man travels from his home to the office at 3 km/hr and reaches his office 30 min late. If the Speed had been 9 km/hr he would have reached 20 min early. Find the distance from his home to office?
Solution:
Let the distance between home and office=d
Suppose he reaches the office on time, Time taken=x minutes
Case 1:
When he reaches 30 minutes late, Time taken=x+30
Case 2:
When he reaches the office 20 minutes early=x-20
As the distance traveled is the same, the ratio of the speed in case 1 to case 2 will be inverse of the time taken in both cases Ratio of Speed in both cases = 3:9 = 1:3
The ratio of Time in both cases = 3:1
Therefore (x+30)/(x-20)=3/1
3x+90 = x -20
2x= 110
x=55 minutes
Taking case 1,
We know that speed=distance/time
4= d/(85/60)=> d= 240/85 = 2.82 km

Example 6.
A bus travels at a speed of 65 km/hour. How far will it travel in 48 minutes?
Solution:
Given,
Speed = 65 km/hour
Time = 48 minutes
= 48/60 Hour (Since we know, 1 hour = 60 minutes)
= 4/5 hour
Distance = speed × time
= 65 × (4/5) km
= (65 × 4)/5 km
= 52 km.

Example 7.
A person travels from one place to another at 50 km/hr and returns at 150 km/hr. If the total time taken is 5 hours, then find the Distance?
Solution:
Here the Distance is constant, so the Time taken will be inversely proportional to the Speed.
The ratio of Speed is given as 50:150, i.e. 1:3
So the ratio of Time taken will be 3:1.
Total Time taken = 5 hours; Time taken while going is 3 hours and returning is 1 hour.
We know that distance=speed × time
Hence, Distance = 50 x 3 = 150 km

Example 8.
A scooter travels at a speed of 65 km per hour. What is the distance covered by the scooter in 4 minutes?
Solution:
Given,
speed=65 km per hour
=65 x 1000/60
=6500/6= 1083.33
Distance covered in 4 minutes=4 x 1083=4333.2 metre.

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