SOLUTION: It takes Leon 17 hours to seal his driveway working by himself. If Michael helps​ Leon, they can seal the driveway in 5 hours. How long would it take Michael to seal the driveway

Algebra ->  Equations -> SOLUTION: It takes Leon 17 hours to seal his driveway working by himself. If Michael helps​ Leon, they can seal the driveway in 5 hours. How long would it take Michael to seal the driveway      Log On


   

Question 1205973: It takes Leon 17 hours to seal his driveway working by himself. If Michael helps​ Leon, they can seal the driveway in 5 hours. How long would it take Michael to seal the driveway​ alone?
Found 3 solutions by ikleyn, josgarithmetic, math_tutor2020:
Answer by ikleyn(52787) About Me  (Show Source):
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.
It takes Leon 17 hours to seal his driveway working by himself.
If Michael helps​ Leon, they can seal the driveway in 5 hours.
How long would it take Michael to seal the driveway​ alone?
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Their combined rate of work is 1/5 of the job per hour.

Leon's rate of work is 1/17 of the job per hour.

Hence, Michael's rate of work is the difference

    1%2F5 - 1%2F17 = 17%2F85 - 5%2F85 = 12%2F85  of the job per hour.


It means that Michael needs  85%2F12 = 71%2F12 hours = 7 hours and 5 minutes

to complete the job working alone.


ANSWER.  Michael needs  7 hours and 5 minutes to complete the job working alone.

Solved.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Michael & Leon, 1%2F5 job per hours

Leon alone, 1%2F17 job per hours

m, the time for Michael working alone
1%2F17%2B1%2Fm=1%2F5
1%2Fm=1%2F5-1%2F17
1%2Fm=17%2F85-5%2F85
1%2Fm=12%2F85
m=85%2F12
m=7%261%2F12

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's say the driveway is 170 square feet in area.
Feel free to pick any other positive real number.
It turns out the driveway area doesn't affect the final answer.

If Leon takes 17 hours to do the job by himself, then his unit rate is 170/17 = 10 square feet per hour.
The formula is: unit rate = (amount done)/time

Assuming neither worker hinders the other, the two men work together at a combined rate of 170/5 = 34 square feet per hour.

Michael's unit rate when working alone is 34-10 = 24 square feet per hour.
This is because each person's unit rate combine together to get 34 square feet per hour.

So Michael will take 170/24 = 85/12 = 7 & 1/12 hours if he works alone.
The formula here is: time = (amount done)/(unit rate)

That mixed number 7 & 1/12 hours is a bit clunky in my opinion.
Let's convert to hours+minutes format.
1 hour = 60 min
1/12 of an hour = 60*(1/12) = 5 minutes
So 7 & 1/12 hour = 7 hours + 5 minutes

Or if you wanted purely minutes,
1 hour = 60 min
7 hours = 7*60 = 420 min
7 hours + 5 min = 420 min + 5 min = 425 min
Note that 425/60 = 85/12