Megan and Sam together take 12 minutes to wash a car. Washing the car by herself took Megan 21 minutes. How long would it take Sam to wash the car?
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To find out how long it would take Sam to wash the car, we can subtract Megan's time from the total time it takes both of them together.
Megan takes 21 minutes to wash the car.
Megan and Sam together take 12 minutes to wash the car.
So, Sam's time to wash the car can be calculated as:
Sam's time = Total time - Megan's time
Sam's time = 12 minutes - 21 minutes
However, since the result would be negative, it means that Sam cannot wash the car alone in less time than Megan.
To find out how long it would take Sam to wash the car, we need to calculate his individual time.
Let's assume that Sam takes x minutes to wash the car.
According to the information given, Megan and Sam together take 12 minutes to wash the car, so their combined work rate is 1/12th of the car washed per minute.
On the other hand, Megan takes 21 minutes to wash the car alone, so her work rate is 1/21th of the car washed per minute.
Using the concept of work rate, we can set up an equation:
Megan's work rate + Sam's work rate = Combined work rate
1/21 + 1/x = 1/12
Now, let's solve the equation for x to find out how long it would take Sam to wash the car:
1/21 + 1/x = 1/12
Multiply all terms by 12x to eliminate the denominators:
12x/21 + 12x/x = 12x/12
Simplify:
12x/21 + 12 = x
Multiply through by 21 to eliminate the fraction:
12x + 252 = 21x
Subtract 12x from both sides:
252 = 9x
Divide both sides by 9:
x = 28
So, it would take Sam 28 minutes to wash the car by himself.
1/both = 1/megan + 1/sam
1/12 = 1/21 + 1/s
s = 28