ExplanationDo not just average the three speeds, as Rajesh spent more time at slower rates than at higher rates, weighting the average toward the slower rate(s). To compute the average speed for a trip, figure out the total distance and divide by the total time.

Pick a convenient distance from home to school, one that is divisible by 30, 40, and 60—say 120 miles (tough for Rajesh, but easier for you).

The first part of the journey (from home to school) took \(\frac{120}{30}= 4\) hours.

The second part of the journey took \(\frac{120}{40}= 3\) hours.

The third part of the journey took \(\frac{120}{60}= 2\) hours.

The total distance Rajesh traveled is 120 + 120 + 120 = 360 miles.

The total time was 4 + 3 + 2 = 9 hours. Finally, his average speed for the entire trip was = 40 miles per hour.

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Sandy

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