Question

A motorcycle is used to reach a particular distance in 5 hours at an average speed of 54 kph. By how much should the average speed be increased to cover
the same distance in 3 hours? ​

Answer 1

Answer:

25 m/s.

Step-by-step explanation:

For 1st case: time = 5 hours = 5×60×60 s = 18000 s.

speed = 54 km/h = (54×1000)/(60×60) = 15 m/s

so, distance = speed×time = 18000 × 15 m

For 2nd case: time = 3 hours = 3×60×60 s = 10800 s

distance = 18000 × 15 m

so, speed = distance/time = (18000×15)/(10800) = 25 m/s.

Answer 2

Concept

Average speed is defined as the total distance travelled by the object in a particular time interval . Average speed doesn't have any direction hence it it scalar quantity.

Average Speed = Distance travelled / Time taken

Given

A bike covers a distance in 5 hrs with average speed of 54 kph.

Find

By how much the average speed must be increased to cover the same distance in 3 hrs.

Solution

Average Speed = Distance travelled / Time taken

Case 1)

Average Speed = 54 kph

Time taken = 5 hrs

Let the distance travelled be x km

x = Avg speed *  Time taken

x = 54 * 5

x = 270

Hence the distance travelled is 270 kms.

Case 2)

Avg speed = ?

Time taken = 3 hrs

Distance = 270 kms

Avg speed  = 270 / 3

Avg speed = 90 kph

Increase in speed = Avg speed final - Avg speed initial = 90 -  54  = 36

The average speed must be increased by 36kph to cover the same distance in 3 hrs.  

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