The second worker did not produce 16 parts in 8 hours, which means it will produce more than 2 parts every hour. Secondly, the 5 minutes is the time difference in producing one part between first and second worker so it could not be that 2 parts are produced in 5 minutes every hour. Did I miss something please?

Let the 2nd worker takes x hrs to complete one part , a/c to ques 1st worker will take ( x + 5/60) = ( x + 1/12) hrs to complete one part.

So in 1 hr 2nd worker completes 1/x parts
and in 1 hr 1st worker completes 1/ ( x + 1/12) parts

According to the question in 8 hrs the 2nd workers produces 16 more parts than 1st worker.

So in 8 hrs 2nd worker completes 8* (1/x) parts ----- A
And in 8 hrs 1st worker completes 8 * ( x + 1/12) parts .------ B

According to the question 8/x parts = 8/ ( x + 1/12) + 16

after solving we get the following quadratic equation
24 *x square + 2*x - 1 =0

Solving the above quadratic equation we get x = 1/6 and x = -1/4
since x can not be negative so 1/x can not be negative . so x = 1/6.

Now we have to find total parts produced by both workers in 8 hrs , which shall be adding A and B.

we get 8/1/6 + 8/ ( x + 1/12) , solving we get value as 48 + 32 = 80.

Should not the answer be 80. What am I missing here. Need help !!

Worker 1: creates 1 part in (x+5) mins. So, 1/(x+5) parts is created in 1 min. This means 480/(x+5) parts in 8 hrs.
Worker 2: creates 1 part in x mins. So, 1/x parts is created in 1 min. This means 480/x parts in 8 hrs.

(480/x)-(480/(x+5))=16
x=10
In 16 hrs, worker 1 creates 32 parts and worker 2 creates 48 parts. Total: 80.
What am I missing here? Carcass

Let the number made by slower worker be x, so the more productive worker makes x+16.

Time taken by both is 8 hrs or 480 minutes.

The difference in their time to make one unit is 5 minutes => \(\frac{480}{x}-\frac{480}{x+16}=5\)

\(480(x+16)-480(x)=5(x)(x+16)\)

\(96*16=x^2+16x\)

\(x^2+16x-48*32=0\)

\((x+48)(x-32)=0\)

So x can be 32 or -48, but x cannot be negative.

Based on your solution, if x=32,

That means the total parts made by both workers is 32+16 =48.

Infact the same thing pointed out by chetan2u in his solution

https://gmatclub.com/forum/two-workers- ... l#p2799927