BTGmoderatorDC wrote:While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

A. 40
B. 60
C. 80
D. 120
E. 160

9am-10am:
Since Harry reaches checkpoint P at 9am -- and travels at rate of 30 mph -- from 9am to 10am Harry travels 30 miles beyond checkpoint P.
Thus, when Ron reaches checkpoint P at 10am, he is 30 miles behind Harry.

Checkpoint Q:
When people compete, SUBTRACT THEIR RATES.
Every hour Ron travels 40 miles, while Harry travels only 30 miles.
Difference between their rates = 40-30 = 10 mph.
Since every hour Ron travels 10 more miles than Harry, every hour Ron catches up to Harry by 10 miles.
Since Ron is 30 miles behind Harry at 10am, and he catches up to Harry at a rate of 10 mph, the time for Ron to catch up to Harry = 30/10 = 3 hours.
Since it takes 3 hours after 10am for Ron to catch up to Harry at checkpoint Q, the time at which Ron catches up to Harry = 10am + 3 hours = 1pm.

1 pm:
Since the professor's rate = 15 mph, the distance traveled by the Professor in the 5 hours between 8am and 1pm = 5*15 = 75 miles.
Thus, at 1pm -- when Ron reaches checkpoint Q and catches up to Harry -- the professor is 75 miles ahead of Ron.
Here, the catch-up rate = (Ron's rate) - (Professor's rate) = 40-15 = 25 mph.
Thus, the time for Ron to catch-up to the Professor = 75/25 = 3 hours.
Since Ron travels beyond checkpoint Q at 40 mph for 3 hours, the distance traveled by Ron after checkpoint Q = 40*3 = 120 miles.

The correct answer is D.