## mikaela19900630 2 years ago Mary takes three hours to mow the yard. It takes Sally five hours. How long would it take with them mowing it together? Can someone help me work my way to the answer please? thanks

1. LogicalApple

A comprehensive approach would be to determine the rate at which Mary mows the yard and the rate at which Sally mows the yard. Then add up the two rates. Based on the information, at what rate does Mary mow a yard ?

2. mathdude69

Think of both of them in terms of how much they get done in an hour. Mary mows 1/3rd of the lawn in an hour Sally mows 1/5th of the lawn in an hour How much of the lawn can they mow together in an hour? How many times must they do that to mow the entire lawn?

3. mikaela19900630

so i would ad the 1/3 and 1/5 together??

4. mikaela19900630

@blondie16

5. LogicalApple

If you add up the two rates you get a combined rate in "yards per hour". Swap the fraction to get "hours per yard".

6. mikaela19900630

wait so i would do 3/1 +5/1 ??

7. LogicalApple

What did you get for the two rates? @mathdude69 told you what they were, so you just have to add them up :)

8. mikaela19900630

so 8/2?

9. LogicalApple

Let's see . . . Mary's rate is 1/3 yard per hour Sally's rate is 1/5 yard per hour So their combined rate is: 1/3 + 1/5 = 8/15 The combined rate they both mow a lawn is 8/15 yard per hour Or, equivalently, 15/8 hours per yard = 1.875 hours per yard.

10. mikaela19900630

wait how doe we get the 15?

11. LogicalApple

Because 1/3 + 1/5 is 8/15. You cannot add fractions unless they have a common denominator. $\frac{ 1 }{ 3 } = \frac{ 5 }{ 15 }$ $\frac{ 1 }{ 5 } = \frac{ 3 }{ 15 }$ $\frac{ 1 }{ 3} + \frac{ 1 }{ 5 } = \frac{ 5 }{ 15 } + \frac{ 3 }{ 15 } = \frac{ 8 }{ 15 }$

12. mikaela19900630

oh okay thank you