Problem Solving

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 rateof 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

OG 79
Ans A

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

In the solution below, the units in red CANCEL OUT.

Time to travel 3.25 miles at a rate of 8 minutes per mile = 3.25 miles * (8 minutes)/(1 mile) = (3.25)(8) minutes = 26 minutes.

Since Bob travels for 50 more minutes -- for a total of 76 minutes -- the total distance traveled = 76 minutes * (1 mile/8 minutes) = 76/8 miles = 19/2 miles.

Since half the total distance is traveled in each direction, the total distance traveled south = (19/2) * (1/2) = 19/4 miles.

Since 3.25 miles south have already been traveled, the additional distance traveled south = 19/4 - 3.25 = 19/4 - 13/4 = 6/4 = 1.5 miles.

The correct answer is A.

To use r*t = d -- where r is in terms of MILES PER MINUTE -- we could proceed as follows:

d = 3.25 miles.
r = 1 mile per 8 minutes = 1/8 mile per minute.
Since t = d/r, we get:
t = (3.25)/(1/8) = (3.25)(8) = 26 minutes.

Since Bob travels for an additional 50 minutes -- for a total of 76 minutes -- at a rate of 1/8 mile per minute, we get:
Total distance = r*t = 1/8 * 76 = 19/2 miles.

From here, we could proceed as in my solution above.