Problem Solving

tapanmittal wrote:Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, by what percent will x have to decrease so that A and B together
can complete the job in 3y/8 hours?
(A) 15%
(B) 25%
(C) 30%
(D) 62.5%
(E) 85%

Here's an approach that minimizes that calculations required.

First, let y = 1
In other words, Machine B takes 1 hour to complete the job.

If x = 4y, then x = 4(1) = 4
So, Machine A takes 4 hours to complete the job.

We want A and B, working together, to complete the job in 3y/8 hours.
Since y = 1, we want their time to be 3(1)/8 hours.
So, working together, they need to complete the job in 3/8 hours.

IMPORTANT
At the moment, x = 4 (Machine A takes 4 hours to complete the job.)
Let's see what happens if we decrease x by 75%. When we do this, we get 1
In other words, Machine A takes 1 hour to complete the job.

So, if Machine A takes 1 hour to complete the job, and Machine B takes 1 hour to complete the job, then working together, they will complete the job in 1/2 hour.

However, we need them to complete the job in 3/8 hours (we need them to complete the job even faster than 1/2 an hour)
So, we need to decrease the value of x by MORE THAN 75%

Since only answer choice E is greater than 75%, it must be the correct answer.

Cheers,
Brent