# Speed, Distance and Time Related Questions Asked in CAT: Relation between Speed, Time and Distance

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## Relation between Speed, Time and Distance

• Speed basically tells us how fast or slow an object moves.
• It is described as the distance travelled by an object divided with the time taken to cover that distance.

Speed = Distance/Time

This shows that Speed is directly proportional to distance but inversely proportional to time.

Distance = Speed ⚹ Time and,

Time = Distance/Speed

Common examples of Speed, Time and Distance

Example 1:

What is the distance covered by a car travelling at a speed of 40 kmph in 15 minutes?

Solution:

Distance = speed ⚹ time = 40 ⚹ 15/60 = 10 km.

The important point to note is that time given was in minutes, whereas the speed was in kmph.

Therefore, either speed has to be converted to km/min or time has to be expressed in hours.

We have converted time in hours.

15 min = 15/60 hours.

Example 2:

A man covers a distance of 600m in 2min 30sec. What will be the speed in km/hr. ? Solution:

Speed = Distance/Time ➾ Distance covered = 600m, Time taken = 2min 30sec = 150sec Therefore, Speed = 600/150 = 4 m/sec

➾ 4m/sec = (4 ⚹ 18/5) km/hr. = 14.4 km/hr.

Example 3:

A boy travelling from his home to school at 25 km/hr. and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.

Solution:

In this question, distance for both speed is constant.

➾ Average speed = (2xy/x + y) km/hr. , where x and y are speeds

➾ Average speed = (2 ⚹ 25 ⚹ 4) / 25 + 4 = 200/29 km/hr.

Time = 5hours 48min = 29/5 hours

Now, Distance travelled = Average speed ⚹ Time

➾ Distance Travelled = (200/29) ⚹ (29/5) = 40 km

Therefore, distance of school from home = 40/2 = 20km