Not sure where to post this.... can you please help me?? NOT the sane as the other

12-year-old-poet

12-year-old-poet

Junior Member
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Jan 25, 2012
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Alex takes 3 hours longer to complete a certain job than Barry does. If they can complete the job
by working together in 3.6 hours, how long would it take Alex to complete the job working
alone?
 
Alex takes 3 hours longer to complete a certain job than Barry does.
Click to expand...

Immediately assign variables to the time that Alex and Barry take to do the job. Say the time Alex takes is a, and the time that Barry takes is b.

Thus, a = b + 3

You need to add 3 to the time of Barry so that the time of both persons are equal. (eg. if Alex takes 5 hours, Barry would take 2 hours and a = b + 3 would work because 5 = 2 + 3)

If they can complete the job by working together in 3.6 hours, how long would it take Alex to complete the job working alone?
Click to expand...

This is where a handy little formula can be used. For things like that (time taken to so something alone and time taken to so the same thing with other people), you can use this:

\(\displaystyle \displaystyle \frac{1}{a} + \frac{1}{b} = \frac{1}{T}\)

T is the time they take if they work together. Say there was another person Cyrus also working, and c were the time he usually takes alone to complete the job, then you could still use the formula, but like this:

\(\displaystyle \displaystyle \frac{1}{a} + \frac{1}{b} + \frac{1}{c}= \frac{1}{T}\)

It's easy, right? :)

Now, you've got:

\(\displaystyle a = b + 3\)

and

\(\displaystyle \displaystyle \frac{1}{a} + \frac{1}{b} = \frac{1}{3.6}\)

Simultaneous equations, solve for a :)
 
Okay, do you understand why the first equation is

a = b + 3

?

Bear in mind that 'a' is the time taken for Alex to complete the job alone, and 'b' is the time taken for Barry to complete the job alone.
 
Okay, I guess it's the second part which bothers you.

If you want, I'll go into the process of deriving it.

So... Alex takes 'a' hours to complete the job alone.
Barry takes 'b' hours to complete the same job alone.

Going by the standard rate formula, we know that "Total work done = Rate of work done x Time taken".
(Similar to "Total distance travelled = Speed x Time")

Let's say that the total work to be done is '100'. The rate of completion of work of Alex would be: Rate = 100/a

To take actual numbers, say Alex takes 5 hours to complete the work '100'. He would be working at a rate of 100/5 = 20/hour. Makes sense?

Using the same logic, Barry would be having a rate of 100/b. Let's say he takes 2 hours. The rate would be 50/hour

Let's say they now work together. This means that they are adding their rates. In one hour, Alex would be doing '20' of the '100' and Barry would do another '50' of the '100' for a total of 70 in one hour! This means their rates were added up.

This brings it back to:

Rate of Alex + Rate of Barry = Rate work is being done

Substitute what we know:

100/a + 100/b = t

Where t is their combined rates. The work, however is still 100, and thus, the time, T, to complete the work together (using the rate formula) would be:

\(\displaystyle 100 = t \times T\)

t = 100/T

Thus we have:

100/a + 100/b = 100/T

We have a common numerator and it was a number we introduced anyway. This can be cancelled:

1/a + 1/b = 1/T

So, maybe the derivation is more complex (I find it more complex myself XD) and I think it's just that you should remember the final formula and understand the steps. Though if you don't understand it straight away, it doesn't matter, you still have time to do so :)

Bottom line,

a = b + 3
1/a + 1/b = 1/3.6

Do you know how to solve those two using simultaneous equations?
 
I can try.... I just emailed my teacher and he said: "With the answer you have provided, it was good enough to let you pass. You have the idea. Your next course is unlocked. Cya later - Mr. Nicholas" As long as I got it right, thank you. Well.... even if I got it wrong thank you for trying to help.
 
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OKay. Just a friggin sec.... Sorry. I had to do some World Geography home work, and I have to take the quiz first.
 
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