Anthony leaves kingstons at 2:00 pm and drives to queensville, 160mi distant, at 45 mph. At 2:15 pm Helen leaves queensville and drives to kingston at 40mph. At what time do they pass each other on the road?

Question

Anthony leaves kingstons at 2:00 pm and drives to queensville, 160mi distant, at 45 mph.  At 2:15 pm Helen leaves queensville and drives to kingston at 40mph.  At what time do they pass each other on the road?

Steve · Accepted Answer

If we place Kingston at (0,0) and Queensville at (0,160), then a time t from when Anthony left, the positions will be equal:

45t = 160-40(t - 1/4)
t = 2

So, they meet at 2:00+2 = 4:00 pm

Or, consider it like this. In the first 15 minutes, Anthony went 45/4 miles. The two cars are approaching each other at 85 mi/hr, so how long does it take to cover the remaining distance?

(160-45/4)/85 = 7/4
That is, they meet 7/4 hours after Helen started.