Answer:
13 hours
Step-by-step explanation:
You want to know the time a car traveling 50 mph has been on the road when a car traveling 65 mph catches up to it, given that the second car started 3 hours later.
Closing time
The first car opens a gap of (50 mi/h)·(3 h) = 150 mi between the cars by the time the second car starts.
The second car closes that gap at the rate of (65 mph -50 mph) = 10 mph.
The time it takes for the second car to overtake the first one is ...
(150 mi)/(15 mi/h) = 10 h
When the second car has been on the road for 10 hours, the first car has been on the road for 13 hours.
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Additional comment
Both cars will have traveled 650 miles when they meet.
(50 mi/h)(13 h) = 650 mi
(65 mi/h)(10 h) = 650 mi
