HELP ANSWER MY QUESTION!

Question

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?

Answer 1

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

 

Answer 2

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