Problema Solution
Sharon drove for part of a 150km trip at 45km/h and the rest of the trip at 75km/h. How far did she drive at each speed if the entire trip took her 2 h 40 min?
Answer provided by our tutors
Let the distance she drove at 45 km/h be x km.
Thus, the distance she drove at 75 km/h will be (150 - x) km.
The time she took to drive the x km will be (x / 45) hours.
The time she took to drive the (150 - x) km will be (150 - x) / 75 hours
Since the total trip took 2h 40mins (which is 8/3 hours), we have:
8 / 3 = (x / 45) + ((150 - x) / 75)
225(8 / 3) = 225[(x / 45) + ((150 - x) / 75)]
600 = 5x + 3(150 - x)
600 = 5x + 450 - 3x
2x = 600 - 450
2x = 150
x = 150 / 2
x = 75 km
150km - 75km = 75km
Hence, Sharon drove 75km at the speed of 75km/h and 75km at the speed of 45km/h.
Let the distance she drove at 45 km/h be x km.
Thus, the distance she drove at 75 km/h will be (150 - x) km.
The time she took to drive the x km will be (x / 45) hours.
The time she took to drive the (150 - x) km will be (150 - x) / 75 hours
Since the total trip took 2h 40mins (which is 8/3 hours), we have:
8 / 3 = (x / 45) + ((150 - x) / 75)
225(8 / 3) = 225[(x / 45) + ((150 - x) / 75)]
600 = 5x + 3(150 - x)
600 = 5x + 450 - 3x
2x = 600 - 450
2x = 150
x = 150 / 2
x = 75 km
150km - 75km = 75km
Hence, Sharon drove 75km at the speed of 75km/h and 75km at the speed of 45km/h.