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Question
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?
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Solution
Let the school be at a distance of x km. If
t1 is the time taken to reach the school, then
`t_1 = "distance"/"average speed" = x/20`
If t2 is the time taken to reach back, then
`t_2 = "distance"/"average speed" = x/30`
Total time,
t = `t_1 + t_2`
= `x/20 + x/30 `
= `x [1/20 + 1/30]`
= `(5x)/60`
= `x/12`
Total distance x + x = 2x
Average speed = `"total distance"/"total time"`
= `(2x)/(x/12)`
= 24 km h-1
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