SOLUTION: Sam can mow a lawn in 30 minutes. Melissa can mow the same lawn in 90 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?

Question 1093210: Sam can mow a lawn in 30 minutes. Melissa can mow the same lawn in 90 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?
Found 3 solutions by Boreal, greenestamps, Alan3354:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
in x minutes, Sam mows x/30 of lawn and Melissa x/90
(x/30)+(x/90)=1 full lawn.
multiply both sides by 90
3x+x=90
4x=90
x=22.5 minutes ANSWER
check
22.5/30+22.5/90=1
Sam will end up doing 3/4 of it and Melissa 1/4 of it.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Boreal gave you a nice explanation of the problem with a good algebraic solution. He also added a comment at the end that can be used to find a different path to the solution.

If you want to be good at math, then always be open to looking at different ways to solve problems. You might find one way is much easier for you (or not...) than another. So let's look at how we can use his last comment to solve the problem differently.

Sam works 3 times as fast as Melissa; so if they work together Sam will do 3/4 of the work and Melissa will do 1/4.

But Sam alone can mow the whole lawn in 30 minutes; so the time it takes him to mow 3/4 of the lawn is 3/4 of 30 minutes, or 22.5 minutes.

So with Melissa helping him, they can mow the lawn together in 22.5 minutes.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Or look at it like this:
Sam's work is that of 3 Melissas --> 4 Melissas.
90/4 = 22.5 minutes

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