AAPL wrote:Manhattan Prep

Half an hour after Car A started traveling from Newtown to Oldtown, a distance of 62 miles, Car B started traveling along the same road from Oldtown to Newtown. The cars met each other on the road 15 minutes after Car B started its trip. If Car A traveled at a constant rate that was 8 miles per hour greater than Car B's constant rate, how many miles had Car B driven when they met?

A. 14 miles
B. 12 miles
C. 10 miles
D. 9 miles
E. 8 miles

OA A

Say the speed of Car B is B mph; thus, the speed of Car A = (B + 8) mph

In 1/2 hour, Car A would travel 1/2*(B + 8) = (B + 8)/2 miles

Thus, both cars together have to cover a distance of [62 - (B + 8)/2] miles

Since Car A and Car B are traveling in opposite directions, their relative speed would be the addition of their speeds.

Relative speed = A + B = (B + 8) + B = (2B + 8) mph

Time to meet = Distance covered / Rel speed = [62 - (B + 8)/2] / (2B + 8) hour

=> [62 - (B + 8)/2] / (2B + 8) = 15 minutes = 15/60 hours

=> B = 56 mph

Thus, Car B would meet Car A after traveling 56 mph * 15 min = 56*15/60 = 14 miles

The correct answer: A

Hope this helps!

-Jay
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AAPL wrote:Manhattan Prep

Half an hour after Car A started traveling from Newtown to Oldtown, a distance of 62 miles, Car B started traveling along the same road from Oldtown to Newtown. The cars met each other on the road 15 minutes after Car B started its trip. If Car A traveled at a constant rate that was 8 miles per hour greater than Car B's constant rate, how many miles had Car B driven when they met?

A. 14 miles
B. 12 miles
C. 10 miles
D. 9 miles
E. 8 miles

OA A

Let's let the rate of Car B be v. Then, the rate of Car A is v + 8.

Since Car A had been traveling for 30 minutes when Car B started its trip and since the two cars met 15 minutes after, the total travel time for Car A is 30 + 15 = 45 minutes = 3/4 hour, and the total travel time for Car B is 15 minutes = 1/4 hour. Since the sum of the distances traveled by the two cars must equal the total distance between the two towns, which is 62, we can create the following equation:

(v + 8)(3/4) + v(1/4) = 62

Let's multiply each side of this equation by 4:

(v + 8)(3) + v = 248

3v + 24 + v = 248

4v = 224

v = 56

Since the rate of Car B is v = 56 mph and since Car B traveled for 1/4 hour when the two cars met, Car B traveled 56 * 1/4 = 14 miles.

Answer: A