GMAT QUANT: Work Problem

Question

A machine produced widgets for two days. On the second day the machine worked for 2 hours longer and at a constant rate 10 widgets per hour faster than it produced on the first day. If during the two days the machine produced a total of 430 widgets and worked a total of 14 hours, what was its constant rate, in widgets per hour, on the first day?

A) 14

B) 21

C) 25

D) 28

E) 35

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Answer 1

Work = rate * time

We know that the machine worked a total of 14 hours and 2 hours more on Day 2 than Day 1 - so, 6 hours for Day 1 and 8 hours for Day2. The rates are r for Day 1 and (r+10) for Day 2. THus, we have:

Day 1 - 6r

Day 2 - 8(r+10)

The total made is 430 and that is comprised of 6r and 8(r+10) ==> 6r + 8(r+10) = 430

6r + 8r +80 = 430

14r = 350

r = 25

The question asks what the rate was for Day 1, which is r - Answer is C) 25

Answer 2