work and motion problems

[Lattefah84]

I will write two solved tasks, and I just ask for an explanation (because, I would not do the 2nd task as it is done.


1st task: Sue can paint a room in 4 hours, and Sam can paint the same room in 5 hours. How long would it take them to paint the room together?

Solution:

Sue paints the room in 4 hours, so she does 1/4 of the room per hour, and Sam does 1/5 of the room per hour If w=t*r
(w-work, r- rate of work, t-time; rate of fork is constant person's work)



t/4 + t/5 =1

5t+4t=1

9t= 20

4= 29/9


2nd task: Abe and ben , working together, can build a cabinet in 6 days Abe works as twice as fast as Ben. How long would it take each of them to build an identical cabinet on his own?


Solution:

t=time for Abe, 2t= time for Ben.


6/t + 6/2t= 1

12+6= 2t

18=2t

9=t

Why is there 1/4*t in first task, and 6/t in second task? How can one explain this? I would do in second task like 1/6*t...?

[satish.nagdev]

pardon me I'm confused what you are asking here. anyway general work related formula is

say x = hours person A needs to do work
y = person B

so individually each of them can do 1/x and 1/y piece of work in 1 hour

and together they can do 1/x + 1/y work in one hour and total time they would need is

xy/x+y

[Lattefah84]

pardon me I'm confused what you are asking here. anyway general work related formula is

say x = hours person A needs to do work
y = person B

so individually each of them can do 1/x and 1/y piece of work in 1 hour

and together they can do 1/x + 1/y work in one hour and total time they would need is

xy/x+y

I asked, why in the first task there is x/4, and y/5, but in the second task there is 6/x and 6/2x ?

[satish.nagdev]

ok got it now
basically in second 6 = combined time so in one hour they'll do 1/6 work

1/t + 1/2t = 1/6, then both sides are multiplied by 6 to simplify.

remember formula

1/x + 1/y = 1/k where x=time for first person alone , y = time for second person alone and k=time for both

hope its clear now.

[sal2]

I think that if you think about what you are solving for conceptually it will help. In the first problem, you know r for each person and you want to find t for them together. So you find the combined r for 1 job and solve for t. In the 2nd problem, you know t for doing the job combined and you need to find the individual rates, which is 6/r + 6/2r. How do you define r? Well, r=t/w. So if w=1, then r=t. Plugging that back in you get 6/t + 6/2t. That's why the t is on top in the first problem and on the bottom in the second. This is one of those questions that will make your head spin, but if you focus on the formulas and what you are solving for conceptually, you should be able to keep it straight.

[Alfred]

Here, two type of tasks is mentioned, in first task Sue can paint a room in4 hrs.
so, in 1 hour Sue can paint 1/4 of the room
Now in the second task, sam can paint the same room in 5 hrs,
so, in 1 hour sam can paint 1/5 of the room

Now if they paint the room together then, in 1 hour they will paint (1/4 + 1/5) = 9/20 of the room

they can together paint 9/20 of a room in 1 hour
so, they can paint whole room in 1/(9/20),
i.e. in 20/9 hours
i have seen this type of problems on TestCircle.com in sample videos