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Question

There are two trails near Vicky's house that she runs regularly, a short loop and a long loop. Last week, she ran 2 short loops and 2 long loops, for a total of 24 kilometers. This week, she ran 6 short loops and 1 long loop, covering a total of 37 kilometers. What is the length of each loop?

The short loop has a length of
kilometers, and the long loop has a length of
kilometers.

Answer 1

You have two equations that can help you solve this problem.

 

2S + 2L = 24  --> 2 short loops plus 2 long loops equals 24 km

6S + 1L = 37

You can plug one of these into the other, but first solve for one variable.

So 2S = 24 - 2L 

S = 12 - L

 

Plug this into equation 2

 

6(12 - L) + L = 37

72 - 6L + L = 37

72 - 5L = 37

-5L = -35

L = 7

S = 12 - L = 12 - 7 = 5