<PRE><B>Question 86544</B>
It takes Peter 15 minutes longer than Charles to mow the lawn by himself. Together, they can mow the lawn in 18 minutes. How long will it take Charles to mow the lawn by himself?
:
Let t = time required by Charles to mow by himself
Then
(t+15) = time required by Peter to do it by himself
:
Let the completed job = 1:
:
{{{18/((t+15))}}} + {{{18/t}}} = 1
:
Multiply equation by t(t+15)
18t + 18(t+15) = t(t+15)
18t + 18t + 270 = t^2 + 15t
36t + 270 = t^2 + 15t
0 = t^2 + 15t - 36t - 270
:
t^2 - 21t - 270 = 0; a quadratic equation
Factors to:
(t - 30)(t + 9) = 0
:
t = +30 min; this is the solution that makes sense
:
:
Check:
18/30 + 18/45 =
 .6 + .4 = 1

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