Problem Solving

Explain

Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 mph. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 mph. If both travelers maintained their speed and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?

A 35 mins
B 45 mins
C 1 hour
D 1 hour 15 mins
E 1 hour 30 mins

John reaches the gas station 15 minutes AFTER Mary.
Thus, when John reaches the gas station, Mary has traveled for 15 minutes BEYOND the gas station.
Distance traveled by Mary in 1/4 of an hour = r*t = (50)(1/4) = 25/2 miles.
Implication:
When John reaches the station, Mary is 12.5 miles AHEAD of John.

Every hour thereafter, John travels 60 more miles, while Mary travels 50 more miles.
To determine when John will catch up to Mary, WRITE IT OUT.

Start:
John = 0 miles, Mary = 25/2 miles.
1 hour later:
John = 0+60 = 60 miles, Mary = 12.5 + 50 = 62.5 miles.
Since John needs more than 1 hour to catch up, eliminate A, B and C.

Answer choice D implies that John needs 15 more minutes to catch up.
15 minutes later:
John = 60 + 60/4 = 75 miles, Mary = 62.5 + 50/4 = 75 miles.
Success!
After 1 hour, 15 minutes, John and Mary have each traveled the same number of miles beyond the gas station, implying that John has CAUGHT UP with Mary.

The correct answer is D.

Alternate approach:

When John reaches the station, Mary is ahead by 25/2 miles.
Thus, John must CATCH-UP by 25/2 miles.

Determine the catch-up rate: the DIFFERENCE between John's rate and Mary's rate.
John's rate - Mary's rate = 60-50 = 10 miles per hour.
Since every hour John travels 10 more miles than Mary, every hour he will CATCH-UP to Mary by 10 miles.

Time for John to catch-up by 25/2 miles = (distance to catch-up)/(catch-up rate) = (25/2)/(10) = 5/4 hours = 1 hour, 15 minutes.

The correct answer is D.