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?

Explanation

Let the distance of school be x km from house of Abdul.
While driving to school,
Average speed `= ("Distance")/("Time")`
`therefore` Time `= ("Distance")/("Average speed")`
`= (x km)/(20 km h ^(-1))`
`= (x)/(20) h " "…(1)`
On return trip,
Average speed `= ("Distance")/("Time")`
`therefore` Time `= ("Distance")/("Average speed")`
`= (xkm)/(30 km h ^(-1))` |
`= (x)/(30) h " "...(2)`
Total distance `= (x + x) km = 2 xkm.`
Total time `= ((x )/(20) + (x)/(30)) h `
`= (3x + 2x )/( 60) h`
`= (5x)/(60) h = (x)/(12) h`
Average speed `= ("Total distance")/("Total time")` `= (2x km)/(x//12 h)`
`= (2x)/(x) xx 12 km h ^(-1) = 24 km h ^(-1)`
The average speed for Abdul.s trip is `24 km h ^(-1).`