Folding Shirts - Folding Speeds [closed]

Steve and Melanie have jobs folding shirts at a store. Every day, they each have 100 shirts to fold. When they finish folding, they can leave. On the first day of the job, Melanie finishes folding in one and a half hours (90 minutes) and leaves, but Steve still has 10 shirts left. The next day, Steve decides to be crafty. When Melanie’s not looking, he moves 5 shirts from his pile to her pile. This means that Melanie will be folding 105 shirts, and Steve 95 shirts. Steve believes he’ll finish at the same time as Melanie, but is surprised when she once again finishes before him.

Assuming that both Steve and Melanie’s folding speeds never change, why was Steve wrong about his prediction?

• This seems to be a pure math question, not a puzzle. – Deusovi Dec 24 '19 at 16:52

Is it because

From the given information:

Melanie takes $$90/100=0.9$$ minutes per shirt, while Steve takes $$90/(100-10)=1$$ minute per shirt.

So for the next day:

With $$105$$ shirts, Melanie requires $$105 \cdot 0.9=94.5$$ minutes, while Steve's $$95$$ shirts take $$95 \cdot 1 = 95$$ minutes. Hence, Melanie will still finish earlier.

Here is an explanation with very little arithmetic.

On the first day

Melanie does 100 shirts in the same time as Steve does 90.

Assuming the same happens on the second day

after the same amount of time they will both have 5 left, which Melanie can do faster than Steve.

His mistake was

dividing the excess shirts evenly between him and Melanie.