SOLUTION: Marvin can shovel the driveway of his family home in 30 minutes. It takes his wife, Nina, 45 minutes to shovel the same driveway. How long would it take to shovel the driveway if t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Marvin can shovel the driveway of his family home in 30 minutes. It takes his wife, Nina, 45 minutes to shovel the same driveway. How long would it take to shovel the driveway if t      Log On


   

Question 36478: Marvin can shovel the driveway of his family home in 30 minutes. It takes his wife, Nina, 45 minutes to shovel the same driveway. How long would it take to shovel the driveway if they were both working together to clear it?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If Marvin can shovel it in 30 minutes, then in 1 minute he can shovel 1/20th of the driveway.

If Nina can shovel it in 45 minutes, then in 1 minute she can shovel 1/45th of the driveway.

Let x = number of minutes it will take them to shovel it off together.
Then in 1 minute, working together they can shovel 1/xth of the driveway.

This means that +%281%2F20%29%2B+%281%2F45%29=+1%2Fx

The LCD for this equation is 180x, so multiply both sides of the equation by 180x.
180x%2A%281%2F20%29%2B+180x%2A%281%2F45%29=+180x%2A%281%2Fx%29
9x+%2B4x+=+180
13x+=+180

Divide both sides by 13:
x+=+180%2F13 minutes or approximately 13.84 minutes.

R^2 at SCC