James and lucas competed in climbing a mountain and coming back. james climbed at an average rate of 3 mph and ran back at 4 mph. lucas climbed at an average rate of 2 mph and ran back at 5 mph. if the path from the bottom to the top of the mountain was 2 miles, how much time did each take to finish and who was faster?

Lucas is faster

Step-by-step explanation:

Distance = speed × time

Time = distance × speed

the path from the bottom to the top of the mountain was 2 miles.

James climbed at an average rate of 3 mph. This means that the time it took James to climb to the top of the mountain would be

2/3 hours

James ran back at 4 mph. This means that the time it took James run back to the bottom of the mountain would be

2/4 = 1/2 hours

Total time that James spent would be

2/3 + 1/2 = 7/6 = 1.7 hours.

Lucas climbed at an average rate of 2 mph. This means that the time it took Lucas to climb to the top of the mountain would be

2/2 = 1 hour

Lucas ran back at 5 mph. This means that the time it took Lucas to run back to the bottom of the mountain would be

2/5 hours

Total time that James spent would be

1 + 2/5 = 1.4hours.