Jan can mow her lawn in 60 minutes by herself. If she hires Wally to do it, he takes 30 minutes, while Peter can do it in 40 minutes. If Jan starts mowing her lawn for 15 minutes then decides to hire Wally and Peter to help her finish, how long will it take (in hours) from when Jan started to when the three finished together?
- First, let's find out how much of the lawn Jan mowed. That's pretty easy. Since it takes her 60 minutes to mow the whole lawn, she mowed 15/60=1/4 of the lawn already. Therefore, 3/4 of the lawn have to be mowed by the three together.
- We now need to find out how much the three can mow together in a certain amount of time. If we knew how much of the lawn each of the three mows in one minute, we could simply add those fractions to get the total amount of mowed lawn per minute.
- We know that it takes Jan 60 minutes to mow the whole lawn. Therefore, she mows 1/60 of the lawn in one minute.
- Wally and Peter can mow 1/30 and 1/40, respectively, in one minute. Now we can simply add the fractions:
1/60 + 1/30 + 1/40 = 9/120
That's how much the three mow in one minute. - They still need to mow 90/120 (=3/4). If it takes them 1 minute to mow 9/120, how much does it take them to mow 90/120?
9/120 --> *10 --> 90/120
1min --> *10 --> 10min - It takes them 10 minutes. Don't forget to add the first 15 minutes Jan mowed alone:
15min + 10min = 25min
Since the question asks for hours we need to convert the minutes:
25min = 25/60h = 5/12h
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