Question

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?

Answer 1

James is faster

Explanation:

It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.

Step-by-step explanation:

Keep in mind that Distance = Speed * Time

First lets starts off with James,

Climbing rate of James = 3 mph

Running back rate of James = 4 mph

Total time taken by James = 3/4 x 2/4 = 14/12 = 7/6

Lets convert that into min to make it easier,

7/6 x 60 = 70 min

Now, lets look at lucas,

Climbing rate of Lucas = 2/2 = 1 hour(s) or 60 minutes

Climbing back rate of Lucas = 2/5 of an hour

Now lets convert this one into minutes,

2/5 x 60 = 24 minutes

Total time taken by Lucas = 24 + 60 = 84 minutes

so that means

James = 70 minutes

Lucas = 84 minutes

Therefore James was faster

Hope this helped and please correct me if I got something wrong :)

Answer 2

Answer:Lucas is faster

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.