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tim washes cars three times slower than bill

by Maria
(Los Angeles, CA, USA)











































tim washes cars three times slower than bill if they both wash 9 cars in one hour how long does it take bill to wash a car

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Jul 01, 2011
Work-Rate Problem
by: Staff


The question:

by Maria
(Los Angeles, CA, USA)

tim washes cars three times slower than bill if they both wash 9 cars in one hour how long does it take bill to wash a car


The answer:

Variables:

x = cars washed by Tim each hour = unknown

y = cars washed by Bill each hour = unknown

t = time in hours = 1

c = cars washed = 9


general equation

x*t + y*t = c


Tim washes cars three times slower than Bill (it takes Tim three times as much time as it takes Bill)

x = y/3


substitute all known values into the general equation

x*t + y*t = c

(y/3)*1 + y*1 = 9


Solve for y

(y/3)*1 + y*1 = 9

(y/3) + y = 9


Multiply each side of the equation by 3

(y/3) + y = 9

3*(y/3) + 3*y = 3*9

y*(3/3) + 3*y = 3*9

y*(1) + 3*y = 3*9

y + 3*y = 3*9

y + 3y = 3*9

y + 3y = 27


combine like terms

y + 3y = 27

4y = 27


divide each side of the equation by 4

4y = 27

4y/4 = 27/4

y*(4/4) = 27/4

y*(1) = 27/4

y = 27/4

y = 6.75

Bill washes 6.75 cars per hour


Time for Bill to wash 1 car = (60 minutes per hour)/(6.75 cars per hour)

Time for Bill to wash 1 car = (60 minutes/6.75 cars)*(per hour)/(per hour)


Notice that the units “per hour” cancel, leaving only minutes in the final answer


Time for Bill to wash 1 car = (60 minutes/6.75 cars)*(1)

Time for Bill to wash 1 car = (60 minutes/6.75 cars)

Time for Bill to wash 1 car = 8.88889 minutes (about 8 minutes and 53 seconds)



The final answer is:

Time for Bill to wash 1 car = 8.88889 minutes (about 8 minutes and 53 seconds)




Thanks for writing.

Staff
www.solving-math-problems.com

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