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A truck headed east 2 hours before a bus headed east from the same location. The rate of the bus was 60 mph and the rate of the truck was 40 mph. How long did it take the bus to get 20 miles ahead of the truck?
Let t = time bus is 20 mi ahead of the truck
Let (t+2) = time the truck will 20 mi behind the bus
Dist = speed * time:
Dist traveled by the truck: 40(t+2)
Dist traveled by the bus: 60t.
We know that the bus will have traveled 20 mi more than the truck
60t - 40(t+2) = 20
60t - 40t - 80 = 20
20t = 20 + 80
20t = 100
t = 100/20
t = 5 hrs when the bus is 20 mi ahead of the truck
60(5) - 40(7) =
300 - 280 = 20 mi