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}](https://tex.z-dn.net/?f=Time%3D%5Cfrac%7BDistance%7D%7BSpeed%7D)
Time took by James for climbing = ![\frac{2}{3}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5C%20hours)
Time took for running back = ![\frac{2}{4}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B4%7D%5C%20hours)
Total time = ![\frac{2}{3}+\frac{2}{4}=\frac{8+6}{12}=\frac{14}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B4%7D%3D%5Cfrac%7B8%2B6%7D%7B12%7D%3D%5Cfrac%7B14%7D%7B12%7D)
Total time taken by James = ![\frac{7}{6}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B6%7D%5C%20hours)
1 hour = 60
Total time taken by James = ![\frac{7}{6}*60=70\ minutes](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B6%7D%2A60%3D70%5C%20minutes)
Time took by Lucas for climbing = ![\frac{2}{2}=\ 1\ hour](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%7D%3D%5C%201%5C%20hour)
Time took by Lucas for climbing = 60 minutes
Time took on return = ![\frac{2}{5} of\ an\ hour=\frac{2}{5}*60=24\ minutes](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%20of%5C%20an%5C%20hour%3D%5Cfrac%7B2%7D%7B5%7D%2A60%3D24%5C%20minutes)
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
Learn more about distance at:
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