# math

Sue can shovel snow from her driveway in 45 minutes. Bill can do the same job in 65 minutes. How long would it take Sue and Bill to shovel the driveway if they worked together?

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1. Add up the "driveways per minute" of the two. That times the time T must equal 1 driveway

1 = (1/45 + 1/65) T
T = 1/(1/45 + 1/65)= 26.6 minutes

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2. Sue = 1/45

Bill = 1/65

Together = 1/x

1/45 + 1/65 = 1/x

We have a fractional equation.

Solve for x.

What is the LCD of 45, 65 and x?

It 585x.

We now multiply every term on BOTH sides of the fractional equation by the LCD.

(1/45)(585x) + (1/65)(585x) = (1/x)(585x)

13x + 9x = 585

22x = 585

Divide BOTH sides of the linear equation (not fractional anymore) by 22 to find x.

x = 585/22

x = 26.59

How long would it take Sue and Bill to shovel the driveway if they worked together?

Answer: 26 hours and 59 seconds, which we can also accept as 27 hours.

Done!

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