Question

James and Lucas competed in climbimg a mountain and coming back. James climbed at an avergate rate fo 3mph and ran back at 4mph. Lucas climed at a average rate of 2 mph and ran back at 5 mph. If the path from the bottom to the top of the moumtaim was 2 miles, how much time did eacch take to finish and who was faster?

Answer 1

Recall that

$\text{spead}=\frac{\text{distance }}{\text{time}}$$\text{time}=\frac{dis\tan ce}{\text{speed}}$

Substitute speed=3mph and distance =2mile, we get

Time taken by James to clime mountain is

$=\frac{2}{3}\text{ hours}$

Substitute speed=4mph and distance =2mile, we get

Time taken by James to run back is

$=\frac{2}{4}=\frac{1}{2}\text{hours}$

$\text{Total time is taken by James =}\frac{2}{3}+\frac{1}{2}=\frac{2\times2}{3\times2}+\frac{1\times3}{2\times3}=\frac{4+3}{6}=\frac{7}{6}=1.17\text{ hour}$

Substitute speed=2mph and distance =2mile, we get

Time taken by Lucas to clime mountain is

$=\frac{2}{2}=1\text{ hour}$

Substitute speed=5mph and distance =2mile, we get

Time taken by Lucas to run back is

$=\frac{2}{5}\text{ hours}$$\text{Total time taken by lucas =1+}\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{7}{5}=1.4hours_{}$

James takes 1.17 hours to finish the race and Lucas takes 1.4 hours to finish the race.

James is faster than Lucas.