SOLUTION: Chuck can shovel the snow off his driveway in 40 minutes. He shovels for 20 minutes and then is joined by Joan. If they shovel the remaining snow in 10 minutes, how long would it h

Question 132050: Chuck can shovel the snow off his driveway in 40 minutes. He shovels for 20 minutes and then is joined by Joan. If they shovel the remaining snow in 10 minutes, how long would it have taken Joan to shovel the driveway alone? I don't want just the answer. If you could provide how you did it and the equations, that would be a life saver. Thanks.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If Chuck shovels the driveway in 40 minutes by himself, that means that every minute he does
one-fortieth (1/40) of the job. Therefore, if he shovels for 20 minutes by himself he does
20*(1/40) = 20/40 = 1/2 the job.
.
This means that when Joan starts to shovel, half the driveway is done. So the remaining amount
of work to be done is 1/2 of the driveway. Joan shovels at some unknown rate each minute. Call
that unknown rate J. Meanwhile Chuck continues at his rate of 1/40 per minute. So if we multiply
these two rates by 10 minutes we get the remaining 1/2 of the driveway done. In equation form
this is:
.
(1/40)*10 + J*10 = 1/2
.
Multiply the entire equation (all terms on both sides) by 40 to get rid of the denominator and
the equation becomes:
.
10 + 400*J = 20
.
Get rid of the 10 on the left side by subtracting 10 from both sides and the equation is:
.
400*J = 10
.
Solve for J by dividing both sides by 400 and the equation is then reduced to:
.
J = 10/400 = 1/40
.
How interesting. Each minute Joan shovels 1/40 of the driveway, the same as Chuck does
each minute. Therefore, if she were working alone it would also take her 40 minutes to
shovel the entire driveway.
.
Hope this helps you to understand the problem a little better.
.

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