Question

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

Answer 1

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 ?

Answer 2

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?

Answer 3

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

Answer 4

@blondie16

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

so 8/2?

Answer 9

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.

Answer 10

wait how doe we get the 15?

Answer 11

Because 1/3 + 1/5 is 8/15. You cannot add fractions unless they have a common denominator.

\[\frac{ 1 }{ 3 } = \frac{ 5 }{ 15 }\]
\[\frac{ 1 }{ 5 } = \frac{ 3 }{ 15 }\]

\[\frac{ 1 }{ 3} + \frac{ 1 }{ 5 } = \frac{ 5 }{ 15 } + \frac{ 3 }{ 15 } = \frac{ 8 }{ 15 }\]

Answer 12

oh okay thank you