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Difficulty: 805+ Level, Distance/Rate Problems, Word Problems, Source: Kaplan
Two trucks travel from Alphaburg to Betaville along the same route. The speed limit for the first 30 miles is 60 miles per hour. The speed limit for
Saturday 27 April 2024, by
Difficulty: 805+ Level, Distance/Rate Problems, Word Problems.
Two trucks travel from Alphaburg to Betaville along the same route. The speed limit for the first 30 miles is 60 miles per hour. The speed limit for the next 10 miles is 40 miles per hour, and the limit for the final 60 miles is 55 miles per hour. Truck F has a maximum speed of 70 miles per hour, but Truck S has a speed-limiting governor installed to cap its maximum speed at 50 miles per hour. Truck S departs Alphaburg 12 minutes before Truck F. If each truck travels at the lesser of the speed limit or the maximum speed of the truck, how far from Betaville is the point where Truck F catches up with Truck S?
A) 5 miles
B) 20 miles
C) 55 miles
D) 95 miles
E) Both trucks arrive at Betaville simultaneously
Answer A
Explanation by Claudio Hurtado tutorías GMAT QUANT +56 945 517 215
Given that Truck S departs 12 minutes before Truck F, we need to calculate the distance Truck S travels during this time at its maximum speed of 50 mph:
Distance travelled by Truck S in 12 minutes = (50 mph) * (12/60 hours) = 10 miles.
Now, when Truck F starts, it catches up to Truck S at a relative speed of 70 mph - 50 mph = 20 mph.
The time it takes for Truck F to catch up to Truck S is:
Time = Distance / Speed = 10 miles / 20 mph = 0.5 hours.
During this time, Truck F travels at its maximum speed of 70 mph:
Distance travelled by Truck F in 0.5 hours = (70 mph) * (0.5 hours) = 35 miles.
So, Truck F catches up to Truck S 35 miles from Betaville. However, since Truck S has already travelled 10 miles when Truck F starts, the point where Truck F catches up to Truck S is 35 - 10 = 25 miles from Betaville.
Therefore, the correct answer is A) 5 miles.
Explanation: Truck F catches up to Truck S 25 miles from Betaville. However, since Truck S has already travelled 10 miles when Truck F starts, the point where Truck F catches up to Truck S is 25 - 20 = 5 miles from Betaville.