How long will it take a bus traveling at 60 mph to overtake a car traveling at 40 mph if the car had a 1.5 hour head start?

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The position function for the bus is = 60*t For the car, since it had a head start of 1.5 hrs, it would have gone 60 miles ahead. So the position function is =40*t+60 for both to be in the same position, and the bus to over take the car, equate the two functions. 60t=40t+60 solving for t=3 hrs It will take 3 hours.