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

Question

2 years ago

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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:

Mathematics

1 answer:

Bogdan [553] · Answer 1 · 2022-06-03T18:46:10+03:00

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

Step-by-step explanation:

Given,

Climbing rate of James = 3 mph

Running back rate of James = 4 mph

Climbing rate of Lucas = 2 mph

Running back rate = 5 mph

Total distance = 2 miles

We know that;

Distance = Speed * Time

As we have to find, we will rearrange the formula in terms of time

$Time=\frac{Distance}{Speed}$

Time took by James for climbing = $\frac{2}{3}\ hours$

Time took for running back = $\frac{2}{4}\ hours$

Total time = $\frac{2}{3}+\frac{2}{4}=\frac{8+6}{12}=\frac{14}{12}$

Total time taken by James = $\frac{7}{6}\ hours$

1 hour = 60

Total time taken by James = $\frac{7}{6}*60=70\ minutes$

Time took by Lucas for climbing = $\frac{2}{2}=\ 1\ hour$

Time took by Lucas for climbing = 60 minutes

Time took on return = $\frac{2}{5} of\ an\ hour=\frac{2}{5}*60=24\ minutes$

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

Therefore,

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

Keywords: distance, speed

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