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

`=(2)/(3)\text{ hours}`

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

Time taken by James to run back is

`=(2)/(4)=(1)/(2)\text{hours}`

`\text{Total time is taken by James =}(2)/(3)+(1)/(2)=(2*2)/(3*2)+(1*3)/(2*3)=(4+3)/(6)=(7)/(6)=1.17\text{ hour}`

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

Time taken by Lucas to clime mountain is

`=(2)/(2)=1\text{ hour}`

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

Time taken by Lucas to run back is

`=(2)/(5)\text{ hours}`
`\text{Total time taken by lucas =1+}(2)/(5)=(5)/(5)+(2)/(5)=(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.