Atruck traveling at an average rate of 45 miles per hour leaves a rest stop. fifteen minutes later s car traveling at an average rate of 60 miles per hour leaves the same rest stop traveling the same route. how long will it take for the car to catch up with the truck

We write the kinematics equations
 a
 vf = a * t + vo
 rf = (1/2) * a * t ^ 2 + vo * t + ro
 We have then
 For the truck: 
 a = 0 
 vf = vo
 rf = 45t
 For the car:
 a = 0
 vf = vo
 rf = 60 * (t-15)
 Matching rf:
 45t = 60 * (t-15)
 Clearing t:
 45t = 60t-900
 60t-45t = 900
 15t = 900
 t = 900/15 = 60h
 
 it will take for the car to catch up with the truck 60h