Abdulla wrote:Sal and Pat can finish a job together in 3 hours. If Sal can do the job alone in 5 hours, what percent of the job does Pat do when Sal and Pat finish the entire job together?
20%
30%
40%
50%
60%
TIME RATIO:
(time for Sal and Pat together) : (time for Sal alone) = (3 hours) : (5 hours) =
3:5.
RATE RATIO:
Time and rate have a RECIPROCAL RELATIONSHIP.
To complete a job in HALF THE TIME, the work must be produced at TWICE THE RATE.
Thus, the rate ratio for Sal and Pat working together versus Sal working alone must be equal to the reciprocal of the value in blue:
(rate for Sal and Pat together) : (rate for Sal alone) =
5:3.
Implication of the ratio in red:
For every 5 units that Sal and Pat produce together, Sal alone produces 3 units, with the result that Pat alone produces the remaining 2 units.
Since Pat produces 2 of every 5 units, Pat's percent of the job = 2/5 = 40%.
The correct answer is
C.
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