A father and his son can clean the house together in 7 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone
Dad's rate = 1/d
son's rate = 1/s
combined rate = (s+d)/(sd)
1/((s+d)/sd) = 7
sd/(s+d) = 7
7s + 7d = sd
1/(1/s) - 1/(1/d) = 1
s - d = 1 or s = 1+d
sub into the other equation
7(1+d) + 7d = d(1+d)
14d + 7 = d + d^2
d^2 - 13d -7 = 0
d = 13.52 hrs
s = 14.52 hrs <------ answer
check: combined rare = (13.52+14.52)/(13.52*14.52) = .1428..
time at combined rate = 1/.1428... = 7
14.5
Yep, 14.5 is also a possible answer, but we usually round to two decimal places, so 14.52 is the preferred answer.
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it has roleplay
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fighting
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1/s + 1/(s-1) = 1/7
s = 14.52