Rates problem

Suz wrote:Can someone help me with this problem?I know the algebraic approach but how can I pick numbers to solve this question?


Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?

Answer choices:

A.(5x – 10z)/2xz


B.2xz/5x - 10z


C.5xz/x + z


D. xz/x + z


E. xz/x + 2z

Answer : B

This is how I did it.

Machine A can complete in x hours => in 1 hour it does (1/x) part of work.

Machine B can complete 1/5th of the work in y hours => it takes 5y hours to complete the work => in 1 hour it does (1/5y) part of work.

Machine A and B can complete 1/2th of the work in z hours => it takes 2z hours to complete the work => in 1 hour they do (1/2z) part of work.

Now just equate (work done by A) + (Work done by B) = Work done by (A+B)
=> (1/x) + (1/5y) = (1/2z)
=>y = 2xz/5x - 10z.

Suz wrote:Can someone help me with this problem?I know the algebraic approach but how can I pick numbers to solve this question?


Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?

Answer choices:

A.(5x – 10z)/2xz


B.2xz/5x - 10z


C.5xz/x + z


D. xz/x + z


E. xz/x + 2z

Let the lot = 20 units.

A alone:
Let x = 5 hours.
Rate for A alone = w/t = 20/5 = 4 units per hour.

B alone:
1/5 of the lot = (1/5)20 = 4 units.
Let y = 4 hours.
Time for B alone = w/t = 4/4 = 1 unit per hour.

A and B together:
When elements work together, add their rates.
z = the time for A+B to produce 1/2 of the lot = 10/(4+1) = 2 hours.

The question asks for the value of y (4 hours). This is our target.
Now we plug x=5 and z=2 into the answers to see which yields our target of 4.

Only answer choice B works:
2xz/(5x - 10z) = (2*5*2)/(5*5 - 10*2) = 20/5 = 4.

The correct answer is B.

Thank you! I read somewhere that you should only pick numbers when there is one variable in the answer choice.Is this true? Is algebra a better approach for this question?