SOLUTION: ethan ran two and a half times as far as conor. will ran 3 more miles than conor. together they ran a total of 27 miles. how far did each run?

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Question 57716: ethan ran two and a half times as far as conor. will ran 3 more miles than conor. together they ran a total of 27 miles. how far did each run?
Answer by ankor@dixie-net.com(22740) (Show Source):
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ethan ran two and a half times as far as conor. will ran 3 more miles than conor. together they ran a total of 27 miles. how far did each run?
:
Let x = dist run by Conor, let e = Ethan's dist; w = Will's dist
:
Knowing the Conor's distance = x, write an equation for each statement:
"ethan ran two and a half times as far as conor"
e = 2.5*x
:
"will ran 3 more miles than conor."
w = x + 3
:
"together they ran a total of 27 miles."
e + x + w = 27
:
"How far did each run?"
In the above equation substitute; 2.5x for e; and (x+3) for w, and you have:
2.5x + x + (x+3) = 27
2.5x + x + x + 3 = 27
4.5x = 27 - 3
4.5x = 24
x = 24/4.5
x = 5.33 mi is the distance run by Conor
:
Ethan:
e = 2.5(5.33)
e = 13.33 mi
:
Will:
w = (5.33 + 3)
w = 8.33 mi
:
Check it: 5.33 + 13.33 + 8.33 = 26.99 ~ 27 mi