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Oliver and Lenny started hiking a hill simultaneously from the bottom to the top. Oliver hiked at a speed of 5 km/h during the first half, then decreased his speed to 4 km/h during the second half. Lenny hiked at a speed of 4 km/h during the first half, then increased his speed to 5 km/h in the second half. Who reached the top of the hill first? What is the proportion of time he spent hiking to that of his friend? The answer is NOT 1:1, so please don't answer that!

 Mar 18, 2021
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Here is my attempt:
Let the distance to top of the hill =D


D/5 + (1/2)D/4 =T, solve for T
T = (13 D)/40 - Oliver's Time


D/4 + (1/2)D/5 =T, solve for T
T = (7 D)/20 - Lenny's Time


Set D = 1
Oliver's Time =13/40 =0.325 =3 1/13
Lenny's Time= 7/20  =0.35 =2 6/7


Conculsion:Lenny reaches the top of the hill first.
Proportion of their hiking time: 2 6/7:3 1/13 =1:1 + 1/13

 Mar 18, 2021

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