Question 171297

I'M NOT FOLLOWING EXACTLY WHAT YOU ARE DOING BUT AT LEAST YOU ARE GIVING IT A SHOT.  TRY TO FOLLOW WHAT I'M DOING:
Let x=hours needed for Bob to repair the machine
Bob works at the rate of 1/x machine per hour
Then x-5=hours needed for Sam to repair the machine 
Sam works at the rate of 1/(x-5) machine per hour
In x-5 hours(1/(x-5))(x-5)=1) Sam completes his machine
In (1/x)(x-5) hours=(x-5)/x =amount of repair done by Bob in (x-5) hours, so:
1-(x-5)/x=(x-(x-5))/x=5/x amount of repair work yet to be done

So, now our final equation to solve is:
(1/(x-5))*3=5/x=
(Rate at which Sam works(1/(x-5)) times the amount of time he works(3 hours)equals the amount of work that he does (5/x))
3/(x-5)=5/x  multiply each term by x(x-5)
3x=5(x-5) =
3x=5x-25  subtract 5x from each side
3x-5x=5x-5x-25
-2x=-25  divide each side by -2
x=12 1/2 hours------------------amount of time needed for Bob to repair a machine
x-5=(12 1/2)-5=7 1/2 hours------------amount of time needed for Sam to repair a machine

CK
In 7.5 hours (amount of time needed for Sam to complete his machine) Bob completes (1/12.5)*7.5=(7.5/12.5 )of a machine, leaving
12.5/12.5 -7.5/12.5=5/12.5 of a machine yet to be done
In 3 hours Sam completes (1/7.5)*3=3/7.5 of a machine
Now the question is does 3/7.5 = 5/12.5???? and the answer is yes!!! they both equal 0.4


Hope this helps---ptaylor