SOLUTION: It takes a boy 90 minutes to mow his father's yard but his sister can do it in 60 minutes. How long would it take them to mow the lawn of they work together, using two lawn mowers?

Question 1049709: It takes a boy 90 minutes to mow his father's yard but his sister can do it in 60 minutes. How long would it take them to mow the lawn of they work together, using two lawn mowers?
Found 2 solutions by advanced_Learner, Theo:
Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
1/90+1/60=1/r
(60+90)/5400=1/r
15/540=1/r
5/180=1/r
r=180/5 using one lawn mower
using two the rate is cut in half
r=90/5

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the boy can mow his father's lawn in 90 minutes, then the boy can mow 1/90 of the lawn in one minute.

if his sister can do it in 60 minutes, then his sister can mow 1/60 of the lawn in 1 minute.

when they work together, then can mow 1/90 + 1/60 of the lawn in one minute.

1/90 + 1/60 is the same as 2/180 + 3/180 which is equal to 5/180 of the lawn in one minute.

5/180 of the lawn in 1 minutes can be simplified to 1/36 of the lawn in one minute.

it would therefore take both of them 36 minutes to mow the lawn.

the basic equation you would use is rate * time = quantity

quantity, in this case, would be 1 lawn.

therefore the basic equation would be rate * time = 1.

for the boy, time is 90 minutes, so the equation becomes rate * 90 = 1.

solve for rate to get rate = 1/90.

for the girl, time is 60 minutes, so the equation becomes rate * 60 = 1.

solve for rate to get rate = 1/60.

rate for the boy is 1/90 of the lawn in one minute.
rate for the girl is 1/60 of the lawn in one minute.

when they work together, their rates are additive, so the rate * time = 1 equation becomes:

(1/60 + 1/90) * time = 1

simplify the rate expression to get 5/180 * time = 1

multiply both sides of the equation by 180/5 to get:

time = 1 * 180/5 = 36 minutes.

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