Vincen wrote:Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip?
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Since the distance traveled at each speed is THE SAME, the distance can be ANY VALUE.
To make the math easier, let the distance at each speed = the LCM of 50 and 75 = 150 miles.
At a speed of 50mph, the time to travel 150 miles = d/r = 150/50 = 3 hours.
At a speed of 75mph, the time to travel 150 miles = d/r = 150/75 = 2 hours.
Average speed for the whole trip = (total distance)/(total time) = (150+150)/(3+2) = 300/5 = 60mph.
The correct answer is
C.
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