# Math

Hello, I have trouble doing this problem:
Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 40 minutes. If she could increase her average speed by 1km/hr, it would reduce her time around the loop by 6 minutes. How many kilometers long is the loop?

So this is what I attempted to do:
I change the 2hours 40 min to 160 mins
then i tried changing it to hours which was 2.6666667
and i tried to plug it in
d=r*t

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1. Let L be the loop distance. Let V be her speed when it takes 2.6667 hours.

You have two unknowns and must combine two equations to get an answer.

At speed V + 1 , she takes 2 hours 34 minutes = 2.5667 hours
At speed V, she takes 2.6667 hours

D = V * 2.6667 = (V+1)* 2.5667
(V+1)/V = 2.6667/2.5667 = 1.03896
V + 1 = 1.03896 V
0.03896 V = 1
V = 25.67 km/h
D = 25.67 * 2.6667 = 68.4 km

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