SOLUTION: For the following problem, define a variable, write and solve an equation, and answer the question: Pat takes 10 minutes longer than Mike to wash the car. Working together, they ca

Algebra ->  Rate-of-work-word-problems -> SOLUTION: For the following problem, define a variable, write and solve an equation, and answer the question: Pat takes 10 minutes longer than Mike to wash the car. Working together, they ca      Log On


   

Question 499035: For the following problem, define a variable, write and solve an equation, and answer the question: Pat takes 10 minutes longer than Mike to wash the car. Working together, they can wash the car in 12 minutes. How long will it take mike to do it alone?
Found 2 solutions by josmiceli, deborabr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In work problems like this, you add rates of
working to get the rate working together
Let Mike's rate = ( 1 car ) / ( m minutes ) = +1%2Fm+
Pat's rate = ( 1 car ) / ( m + 10 min ) = +1%2F%28+m+%2B+10%29+
Their rate working together = ( 1 car ) / ( 12 min ) = +1%2F12+
-------------------
+1%2Fm+%2B+1%2F%28+m+%2B+10+%29+=+1%2F12+
Multiply both sides by +12%2Am%2A%28+m+%2B+10+%29+
+12%2A%28+m+%2B+10+%29+%2B+12m+=+m%2A%28+m+%2B+10+%29+
+12m+%2B+120+%2B+12m+=+m%5E2+%2B+10m+
+m%5E2+-+14m+-+120+=+0+
I'll use the quadratic formula
m+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-14+
+c+=+-120+
m+=+%28+-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2+-+4%2A1%2A%28-120%29+%29%29+%2F+%282%2A1%29+
m+=+%28+14+%2B-+sqrt%28+196+%2B+480+%29%29+%2F+2+
m+=+%28+14+%2B-+sqrt%28+676+%29%29+%2F+2+
+m+=+%28+14+%2B+26+%29+%2F+2+ ( ignore negative root )
+m+=+20+
It takes Mike 20 min working alone
check answer:
+1%2Fm+%2B+1%2F%28+m+%2B+10+%29+=+1%2F12+
+1%2F20+%2B+1%2F%28+20+%2B+10+%29+=+1%2F12+
+1%2F20+%2B+1%2F30+=+1%2F12+
Multiply both sides by 60
+3+%2B+2+=+5+
OK

Answer by deborabr(181) About Me  (Show Source):
You can put this solution on YOUR website!
Pat --> x+10
Mike -> x
Pat + Mike = 12
x + x + 10 = 12
2x + 10 = 12
2x = 12 - 10
2x = 2
x = 1
Mike takes 1 minute to wash the car
Pat takes 11 minutes to wash the car