Marisol will run 10 minutes per hour and Amy will start 5 minutes later running at 8 minutes per hour. The equations for the runners are given as follows, for which M(x) = Marisol and A(x) = Amy
M(x) = 1/10 x
A(x) = 1/8 (x-5) where x is in min and M(x) and A(x) are in miles:
Both are linear equations. You have to find where both lines meet.
M(x) = A(x)
1/10 x = 1/8 (x-5)
1/10 x = 1/8 x - 5/8 (distributive property)
1/10 x - 1/8 x = -5/8 (regrouping the x)
(1/10 - 1/8) x = -5/8
(4/40 - 5/40) x = -5/8 (common denominator is 40)
-1/40 x = -5/8 (you can eliminate the negative signs)
x = 5*40/8 = 200/8 = 25 min
Marisol and Amy meet at 25 minutes.
If you want to know at what distance they meet:
M(25) = 1/10 (25) = 2.5 miles
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