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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?

### 2 Answers by Expert Tutors

Alex S. | Retired, Looking to Share My Love of Mathematics and ComputersRetired, Looking to Share My Love of Mat...
4.8 4.8 (75 lesson ratings) (75)
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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
4r2=2/6
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

Crystal H. | Chemistry and English tutorChemistry and English tutor
4.7 4.7 (93 lesson ratings) (93)
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Hello Kaitlyn.  This is a combined work problem.  The formula for combined work with 2 people is:

(A)(B) = T
A+B

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
2B=24
B=12

The other crew takes 12 hours