There’s a couple of steps we have to take in this question, but all hinge on the same formula.

R*T = W

Let’s look at what we have and what we need.

The rate of two machines is ¼. Because R * 4 = 4. → R = ¼.

We also know that the rate of anything is R = W/T.

This means that 1/x + 1/x = ¼ - because we have two machines.

We are given that one machine is 1.5 times faster than the other. So we can adapt this formula to:

1/x + 1/x *3/2 = 1x+3/2x = ¼ → 5/2x = ¼ → x = 2/20 → x = 1/10.

We know that the rate of one machine is 1/10. And one is faster 1.5x times faster.

1/10x * 3/2 = 3/20.

The rate of the faster machine is 3/20. Let’s fill this in the formula to find out the time for the faster machine.

3/20 * T = 1

T = 20/3.

This is answer choice E

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