a mason's helper requires 6 hours more to pave a concrete walk than it takes the mason. the two worked together for 2 hours when the mason was called away. the helper completed the job in 4 hours. how long would it take each to do the same job if they work separately?
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Answer:
Step-by-steMason does job in m hours. Helper does job in m+4 hours.
t=time in hrs
1/m + 1/(m+4)=(2m+4)/(m^2+4m) = 1/t
3 * (2m+4)/(m^2+4m) = (6m+12)/(m^2+4m) = 3/t
1 - (6m+12)/(m^2+4m) time remaining [1 - 3/t]
2 * 1/(m+4)= 1 - (6m+12)/(m^2+4m)
2/(m+4)=1 - (6m+12)/(m(m+4))
2m=m^2+4m-6m-12
m^2-4m-12=0
(m-6)(x+2)=0
m=6 hr
m+4=10 hr