One lawn care woker can mow 3 lawns in 60 min and another ca

One lawn care woker can mow 3 lawns in 60 min. and another can mow 5 lawns in 75 min. How long will it take them to mow 7 lawns together?

Solution

Let \"the job\" be 1 lawn mowed
Our Man DATA:
time = 20 min/job ; rate = 1/20 job/min
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Other Man DATA:
time = 15 min/job ; rate = 1/15 job/min
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Together DATA:
time = x min/job ; rate = 1/x job/min
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Equation:
rate + rate = together rate
1/20 + 1/15 = 1/x
Multiply thru by 60x to get:
3x + 4x = 60
7x = 60
x = 60/7 minutes (time for both working together to mow one lawn)
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Time to mow 7 lawns = 7(60/7) = 60 minutes or one hour