Question

Two companies working together can clear a parcel of land in 24 hours. Working alone, it would take Company A 10 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone

Answer 1

43 hours 31 minutes

Explanation:

Let the time it takes Company B=x

Company B's Work Rate=1/x

It would take Company A 10 hours longer,Time for A=x+10

Company A's Work Rate=1/(x+10)

The two companies working together can clear a parcel of land in 24 hours.

Their joint work rate=1/24

Therefore:

1/x + 1/(x+10) =1/24

Taking L.C.M

(x+10+x)/(x(x+10)) = 1/24

(2x+10)/(x²+10x)) = 1/24

On Cross multiplication

24(2x+10)=x²+10x

48x+240=x²+10x

x²+10x-48x-240=0

x²-38x-240=0

x= -5.52 or 43.52

Since x>0

x= 43.52 hours

= 43 hours 31 minutes

It would take Company B 43 hours 31 minutes to clear the parcel of land.