Two road crews, working together, repair 1 mile of road in 4 hours. Working separately, one of the crews takes about 6 hours to repair a similar road. How long would it take the other crew, working alone, to repair a similar road?
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r1= 1/6 (mile/hour)= rate of first crew
r2 = ? = rate of other crew (unknown, to be determined)
4 hours * (r1+r2) = 1 mile
4(1/6+r2) = 1
4/6+4r2 = 1
r2=2/(6*4) =2/24 = 1/12 (second crew would complete the 1 mile road i n 12 hours)
CHECK:4*(1/6+1/12) = 4* (2/12 + 1/12) = 4* (3/12) = 12/12 = 1 CORRECT
Hello Kaitlyn. This is a combined work problem. The formula for combined work with 2 people is:
(A)(B) = T
A= time of crew 1
B=time of crew 2
T= time of crew 1 and 2 working together
A=6 B=unknown T=4
6(B)/(6+B) = 4
6B = 4(6+B)
6B = 24 +4B
The other crew takes 12 hours