Work problem

prince11 wrote:Hi,

Can anyone please explain the work problem below? I get confuse when work done is more than 1. Is there a website that has these kinds of problems? Many websites have problems involving 1 work done. Thanks in advance.


Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 4 hours?

(a) 2.4
(b) 3.6
(c) 4.2
(d) 5.5
(e) 6.4

[spoiler]The best answer is E.
2 carpenters build 2 desks in 2.5 hours ---> 4 carpenters build 4 desks in 2.5 hours ----> In 4 hours there are (4/2.5 = 1.6) time units. And (4 x 1.6) is 6.4 desks.[/spoiler]

This site should give you a good primer on work rate problems of different kinds. After reviewing it you should be able to handle this. Give it a try.

https://www.purplemath.com/modules/workprob.htm

I learnt how to do these types of problems based on someone else's post so this method might help you as well.

The trick is to hold 1 variable constant temporarily.

c d h
2 2 5/2 (2.5)

I will choose to hold (hours) constant. and I will divide the rest by 2

so 1 carpenter will be able to do 1 desk in 2.5 hours

c d h
1 1 5/2

Now I want to get the hours to 1, so i will hold the (carpenter) constant, and I will divide desks and hours by 5/2

so now I have 1 carpenter can do 2/5 desks in 1 hour.

c d h
1 2/5 1

I want 4 carpenters so I hold (hours) constant again and multiply carpenters and desks by 4

c d h
4 8/5 1

Lastly I want 4 hours so I hold (carpenters) constant and multiply hours and desks by 4

c d h
4 32/5 4

32/5 = 6.4 desks


I know this is a long explanation but I broke it down step by step so hopefully you can understand this better.

Set up a ratio.

Treat the 2 carpenters as one unit. 1 unit can build 2 desks/2.5 hours. This is the same as (2/2.5)(desks/hour). That fraction looks hideous, so change 2.5 to a fraction and simplify. So we get 1 unit can build (4/5)(desks/hour).

Then 2 units (4 carpenters) will double the rate they build, 2*(4/5)(desks/hour) = (8/5)(desks/hour)

Now set up an equation using these ratios:

(8/5)(desks/hour) = (x/4) (desks/hour)

5x = 32
x = 6.4