SOLUTION: Sam and Bob both repair machines. Sam can repair one machine 5 hours faster than Bob can repair the same machine. If Bob and Sam both work on separate machines until Sam has comp

Question 171297: Sam and Bob both repair machines. Sam can repair one machine 5 hours faster than Bob can repair the same machine. If Bob and Sam both work on separate machines until Sam has completed his. Sam then takes over and finishes Bob's machine in 3 hours. Hint: consider completing two machines as one job.
I know I've messed up, but can't get it correct.
Here's what I've tried:
x is # of hours it takes Sam to complete a machine
x + 5 is the # of hours it takes Bob to complete a machine.
1/x + 1/(x+5) = 1
(x+5 + x)=(x^2 + 5x)
using the quadratic formula I end up with:
x = (-3+/- sq root of 29)/ 2
I know there is something about 5/3 of Bob's work being done, but I am lost.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

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
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