A marzipan factory has two machines producing marzipan. Every day, the two machines operate constantly from 08:00 to 18:00, and produce together N kg of marzipan. What percent of the total amount of marzipan produced by machines W and D together was produced by machine W?
(1) Working alone, it takes machine W twenty five hours to produce (N/2) kg of marzipan.
(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.
If you understand your work-rate concepts well, you can do this without any calculations.
Given: W and D take 10 hrs to complete 1 work (N kg of Marzipan) together. So we know their combined rate of work. If you recall your work rate theory, rates are additive.
Rate of W + Rate of D = Combined Rate
If we get the rate of work of one of the machines, we can easily find the rate of work of the other.
Required: Amount of work done by W/Amount of work done together = Rate of work of W/Combined Rate
Stmnt 1: W takes 25 hrs for 1/2 work.
We now know the rate of work of W. We also have the combined rate. So we have the required ratio
Stmnt 2: To do 1/2 work, W takes twice the time taken by D to do 1 work.
So W takes 4 times the time taken by D to do one work. Since we have ratio of time taken, we get ratio of rates and hence the required rate.
(If you are wondering how,
Ratio of time taken by W:D = 4:1 so rate of work of W:D = 1:4
Rate of work of W/Combined Rate = 1/(1+4) = 1/5)
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