Working together, tow dock workers can load a crate in 6 min. One dock worker...?

Question

Working together, two dock workers can load a crate in 6 mins. One dock worker, working alone, can load the crate in 15 min. How long would it take the second dock worker, working alone, to load the crate?

Answer 1

6/x + 6/15 = 1 ........ [time they work on top, time to do it alone on bottom]

6/x = 9/15
x = 90/9 = 10 min.

Answer 2

The first dock worker loads a crate in 15 minutes. So if he is working for 6 minutes, he has loaded 6/15 = 2/5 of a crate.

Therefore, the other worker must have loaded the rest of the crate: he has loaded 3/5 of a crate within 6 minutes.
So he can load 1/5 in 2 minutes.

Therefore, the second worker needs 10 minutes to load a crate on his own.

Answer 3

The first dock worker has a rate of one unload per 15 minutes (1/15). The second dock worker has a rate of one unload per x minutes (1/x).

Combined they have a rate of one unload per 6 minutes (1/6).

That means that 1/15 + 1/x = 1/6 which is the equation to solve.

Multiply each of the terms by x. That gives x/15 + 1 = x/6
Combine the x terms to get x(1/15 -1/6) = -1

Using common denominators x(2/30 - 5/30) = -1

x(-3/30) = -1 so x/10 = 1/ Solving for x you get x=10 which means that the unknown rate for the second dock worker is 10 minutes to load.

This is independent of the two workers both deciding to take a break and gripe about the low pay they are getting for ship-loading.

Answer 4

Perhaps I am reading too deeply into the problem, but how can one know that from the information provided? It gives you info on how they perform together, assuming these are the same two workers we are speaking of, and how one performs alone. . . neither of which have anything to do with how the remaining worker performs alone. If nothing else, I would simply assume an equivalent performance for planning purposes.

Answer 5

15 minutes.

There is no reason to think that one worker alone pulls more weight than another, and no reason to think that two working together is not more efficient than two working seperately.

I'm inclined to think your teacher is looking for the proportional solution offered by some others, but this is in actuality a terrible question to illustrate that.

Answer 6

No, they won't get baited into pier pressure so easily. They are made of tougher stuff than to succumb to such petty attempt of fishing for acceptance. They ride the big waves of life and swell with high self-esteem. Cheers

Answer 7

is this a joke?

assuming they are of equal ability, 15 min also.

Answer 8

0 min. because he/she is management and would tell someone else to do it