Question

A boy cycle from P to Q at an avarage speed 16km/h. he cycle back at 12km/h find the avarage speed in km/h for the whole trip

Answer 1

Let x denotes the distance from P to Q.

Average speed of one way = 16 km/h

Average speed of the return = 12 km/h

The total distance covered for the whole trip is

`\begin{gathered} total\; distance=x+x \\ total\; distance=2x \end{gathered}`

Recall the relationship between time, distance, and speed.

`time=(distance)/(speed)`

The total time taken for the whole trip is

`\begin{gathered} total\; time=t_1+t_2 \\ total\; time=(x)/(16)+(x)/(12) \\ total\; time=(7x)/(48) \end{gathered}`

The average speed for the whole trip is

`\begin{gathered} avg\; speed=(total\; distance)/(total\; time) \\ avg\; speed=(2x)/((7x)/(48)) \\ avg\; speed=2x\cdot(48)/(7x) \\ avg\; speed=2\cdot(48)/(7) \\ avg\; speed=(96)/(7)\; \end{gathered}`

Therefore, the average speed of the whole trip is 96/7 km/h