Cant get my head around this.
Six machined work at a constant rate and do a job in 12 days. If I want to do the job in 8 days, how many extra workers do I need?
2, 3, 4, 6, or 8
PS Workrate
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Approach 1: Plug in a rate for EACH MACHINESix machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
2
3
4
6
8
Let the rate for each machine = 1 unit per day.
Rate for 6 machines = 6 units per day.
In 12 days, the amount of work produced by 6 machines = r*t = 6*12 = 72 units.
To produce 72 units in 8 days, the required amount of work per day = w/t = 72/8 = 9 units per day.
To increase the rate from 6 units per day to 9 units per day, 3 more machines are needed.
The correct answer is B.
Approach 2: Inverse proportion method
The number of machines is INVERSELY PROPORTIONAL to the number of days:
(machines)(days) = (machines)(days).
As the number of machines INCREASES, the number of days must DECREASE, so that in each case the SAME AMOUNT OF WORK is produced.
Since 6 machines take 12 days, and the job is to be completed in 8 days, we get:
6 * 12 = m * 8
72 = 8m
m = 9.
Since 9 machines are required, the original number of machines -- 6 -- must increase by 3.
The correct answer is B.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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