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If a car traveled from Townsend to Smallville at an average

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If a car traveled from Townsend to Smallville at an average

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Manhattan Prep

If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
2) The distance from Townsend to Smallville is 165 miles.

OA A

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AAPL wrote:
Manhattan Prep

If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
2) The distance from Townsend to Smallville is 165 miles.
Statement 1: The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
Case 1: Distance between Townsend and Smallville = 80 miles
Time to travel from Townsend to Smallville at a speed of 40 mph = 80/40 = 2 hours.
Time to travel from Smallville to Townsend = 2 hours + (50% of 2 hours) = 3 hours.
Since the total time = 2+3 = 5 hours, the average speed for the entire 160-mile trip = 160/5 = 32 miles per hour.

Case 2: Distance between Townsend and Smallville = 160 miles
Time to travel from Townsend to Smallville at a speed of 40 mph = 160/40 = 4 hours.
Time to travel from Smallville to Townsend = 4 hours + (50% of 4 hours) = 6 hours.
Since the total time = 4+6 = 10 hours, the average speed for the entire 320-mile trip = 320/10 = 32 miles per hour.

No matter the distance, the average speed = 32 miles per hour.
SUFFICIENT.

Statement 2: The distance from Townsend to Smallville is 165 miles.
Since the speed from Smallville to Townsend can be any nonnegative value, the average speed for the entire trip cannot be determined.
INSUFFICIENT.

The correct answer is A.

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