After driving to a riverfront parking lot, Bob plans to run

swerve wrote:After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

A. 1.5
B. 2.25
C. 3.0
D. 3.25
E. 4.75

The OA is A

Source: Official Guide

We are given that Bob plans to run south along the river, turn around, and return to where he started.

We know that his run south (from the parking lot) and his run north (back to the parking lot) are equal in distance. We will use this information later in the solution.

We are also given that Bob’s rate is 8 minutes per mile, or, in other words, (since Rate = Distance/Time) his rate is 1 mile per 8 minutes or 1/8.

We are told that Bob has already run 3.25 miles south, and he wants to run for 50 minutes more. Thus, we calculate how far Bob will go in the remaining 50 minutes.

Distance = Rate x Time

Distance = 1/8 x 50

Distance = 50/8 = 25/4 = 6.25 miles

Thus, we know that Bob’s total running distance will be 6.25 + 3.25 = 9.5 miles. Because we know the distance is the same both ways, we know that each leg of his trip is 9.5/2 = 4.75 miles. Since Bob has ALREADY RUN 3.25 miles south, he can run 4.75 – 3.25 = 1.5 miles more. At that point, he will have to turn around and head back north to the parking lot.

Answer: A