Question 1065767: Out of the work man x and y,x is twice as good as y to perform the work assigned to them.If x can finish the assigned work in 40 days less than y,then in how many days they together can finish the work if they work together?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x can finish the work in 40 days less than y.
x works twice as fast as y, if i understood you correctly.
if we let z = the rate of y, then 2z = the rate of x.
rate * time = quantity of work produced.
quantity of work produced = 1 job.
if we let q = the time it takes y to finish the work, then q - 40 is the time it takes x to finish the work.
when y works, the formula becomes z * q = 1
when x works, the formula becomes 2z * (q-40) = 1
if we solve both of these formulas for z, we get:
z = 1/q and z = 1/(2 * (q-40))
simplify to get z = 1/q and z = 1/(2q-80)
this means that 1/q = 1/(2q-80)
cross multiply to get 2q-80 = q
subtract q from both sides of this equaiton to get q-80 = 0
solve for q to get q = 80
when y works, you get zq = 1 which becomes 80z = 1 which becomes z = 1/80.
when x works, you get 2z(q-40) = 1 which becomes 2z(80-40) = 1 which becomes 2z*40 = 1 which becomes 2z = 1/40.
remember now, that the rate of y is z and the rate of x is 2z.
the rate of x is 1/80 of the job in 1 day.
the rate of y is 1/40 of the job in 1 day.
when they work together, their rates are additive, so you get:
(1/80 + 1/40) * q = 1
q in this case is the time it takes when they are working together.
simplify to get 3/80 * q = 1
solve for q to get q = 80/3 = 26 and 2/3 days.
your answer should be that they take 26 and 2/3 days to complete the job when they work together. if i understood your problem correctly.
when x works alone, he takes 40 days to complete the job.
when y works alone, he takes 80 days to complete the job.
x takes 40 days less than y to complete the job, so that part checks out.
the rate of x is 1/40 of the job in one day while the rate of y is 1/80 of the job in 1 day, so the rate of x is twice the rate of y, so that part checks out as well.
i believe that 26 and 2/3 days to complete the job when they work together is the solution you are looking for.
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