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Car A and B started at different times from Town X and travel to Town Y on the same route at different constant speeds. Car A was initially behind Car B, but Car A was faster. Car A passed Car B at 1:30 pm. At 3:15 pm, Car A reached Town Y, and at that moment, Car B was still 35 miles away from Town Y. The time Car B took to complete the trip from Town X to Town Y was 25% more than the time that Car A took. What is the speed of Car A?
Title
Faster car arrives first
Your Result
Incorrect
Difficulty
Very Hard
Your Pace
2:35
Others' Pace
5:17
Video Explanation
Text Explanation
Let A = speed of Car A, and B = speed of Car B.
Start with the information that the same distance took Car B 25% longer than Car A, or 1.25 time longer. The ratio of the times is inversely proportional to the ratio of the speeds, so A = 1.25*B.
Let D be the distance from where the cars pass each other at 1:30 pm to Town Y. Car A covers the distance D in 1 hr 45 min, or 1.75 hr; in that same time period, B covers (D – 35).
Formula for A: D = A*1.75
Formula for B: D – 35 = B*1.75
Substitute the former into the latter, to eliminate D.
A*1.75 – 35 = B*1.75
7A – 140 = 7B
A – 20 = B
Now, substitute A = 1.25*B (it’s easier to solve for B, then find A).
1.25*B – 20 = B
0.25*B – 20 = 0
0.25*B = 20
B = 80 mph
A = 1.25*80 = 100 mph
Answer = (E)
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