# Abdul, while driving to school, computes the average speed for his trip to be 20 km h-1. On his return trip along the same route, there is less traffic and the average speed is 30 km h-1. What is the average speed for Abdul's trip?

## Given that

Abdul, while driving to school, computes the average speed for his trip to be 20 km h-1. On his return trip along the same route, there is less traffic and the average speed is 30 km h-1.

## We need to find

The average speed for Abdul’s trip

## Solution

Let us take the following assumptions for calculating the average speed for Abdul’s trip

### As per given data in the question

Average speed from home to school v1av = 20km h-1
Average speed from School to Home v2av = 30km h-1

### Our assumptions

The distance Abdul commutes while driving from Home to School = s
Let us assume time taken by Abdul to commutes this distance = t1
Distance Abdul commutes while driving from School to Home = S
Let us assume time taken by Abdul to commutes this distance = t2

Also we know that

The time taken from Home to School t1=S/v1av
Similarly Time taken from School to Home t2=S/v2av

### Total distance

Total distance from home to school and backward = 2S——-(i)

Total time taken from home to school and backward (T)=S/20+S/30———-(ii)

## Formula

Speed = Distance  / Time

Therefore,

Average Speed(Vav)for covering total distance (2s)=Total Distance/Total Time

So from equations (i)  and (ii) we get,
Average Speed(Vav) =2S/(S/20+S/30)
=2S/[30S+20S)/600] =1200S/50S
=24kmh-1