SOLUTION: the county's new asphalt paving machine can surface one mile of highway in 10 hours. A much older machine can surface one mile in 18 hours. How long will it take them to surface on

Question 749509: the county's new asphalt paving machine can surface one mile of highway in 10 hours. A much older machine can surface one mile in 18 hours. How long will it take them to surface one mile of highway, working together? How long will it take them to surface 20 miles?
Found 2 solutions by FrankM, josmiceli:
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
First machine can do 1/10 mile per hour, Second machine, 1/18 mile per hour.
1/10 + 1/18 = 9/90 + 5/90 = 14/90 = 7/45 miles per hour.
A full mile would take 45/7 hours or ANS = 6 3/7 hours.
Multiply by 20, 900/7 = ANS = 128 4/7 hours.
Note - another tutor offered a short cut for this type of problem.
A 10 hr worker and a 18 hour worker combined will do a job in (10*18)/(10+18) hours or 180/28 which is the same 45/7 hours I calculate.
To be sure you get the numerator and denominator correct, be sure the answer makes sense. 2 10 hour workers would combine to do a job in 5 hours, so the 10 and 18 combine must be between 5 and 10.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Rate of resurfacing for new machine:
( 1 mile ) / ( 10 hrs )
Rate for older machine:
( 1 mile ) / ( 18 hrs )
--------------------
Let = the time in hours for them to
resurface 1 mile working together

Multiply both sides by

It will take them 6 hrs and 26 min working together
check:

OK
For 20 miles:

It will take them 128 hrs and 34 min
check:

OK
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