working on a 9 day project

Nekkamath

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Jerry worked for one day on a project that he could have completed alone in nine days. Bill joined Jerry the next day, and they worked together for exactly three days to complete the project. How much of the job did Bill do in those three days? Express you answer as a common fraction.

Bill worked 3 out of 4 days, but it could have been done in 9 days which would be 8 out of 9 days for Bill if he was working alone. Jerry worked 1 day out of 4 and 1 day out of 9 possible days.

3/4 x 8/9 = 24/36 = 2/3

I say the answer is 2/3 for how much of the work Bill did.
 
Nekkamath said:
Jerry worked for one day on a project that he could have completed alone in nine days. Bill joined Jerry the next day, and they worked together for exactly three days to complete the project. How much of the job did Bill do in those three days?
Convert the times to rates:

. . .time to complete task (in days):
. . . . .jerry: 9
. . . . .bill: b
. . . . .together: t

. . .portion completed per time unit:
. . . . .jerry: 1/9
. . . . .bill: 1/b
. . . . .together: 1/t

In one day, Jerry did 1/9 of the task, leaving 8/9 to be done.

In three days, Jerry and Bill together completed the remaining 8/9 of the task. Then:

. . . . .(amount done) = (amount done per time unit)*(time units)

. . . . .8/9 = (1/t)(3)

. . . . .t = (3)(9/8) = 27/8

Assuming their labors are additive, we then have:

. . . . .1/9 + 1/b = 1/t = 8/27

Solve for the amount, 1/b, that Bill does per day, and then multiply by the number of days to find the fraction of the task that he completed. :wink:

Eliz.
 
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