# Word Question/s

• Mar 10th 2013, 06:35 PM
Magica
Word Question/s
I've been having trouble with the word questions in algebra. I do fine with the usual algebra questions, but for questions where you have to write the equation yourself, my mind just can't get around how. I'd like general advice on these questions, but I do have a specific one as well (which I'm sure will be obvious once I see the equation, haha):

"A high speed pump and a low speed pump can be used at the same time to fill a swimming pool in 8 hours. If only the low speed is used, it takes 3 hours longer than if only the high speed is used. How long does each pump take to fill the whole pool if used alone?"

I don't know where to even start writing the equation, I think there would be two equations and two variables, but I don't know...

Thank you very much.
• Mar 10th 2013, 07:55 PM
Re: Word Question/s
For word questions, you label your unknowns and then use substitution with one of your equations. For a system of more than two linear equations you can use a matrix or use substitution multiple times.

Let l = time of the low speed pump to fill the pool, h = time of the high speed pump to fill the pool.
Assuming that the relationship is linear when using both the low speed pump and the high speed pump at the same time we get

l = h+3
h+l = 8

then solve.
• Mar 10th 2013, 08:21 PM
Magica
Re: Word Question/s
Quote:

For word questions, you label your unknowns and then use substitution with one of your equations. For a system of more than two linear equations you can use a matrix or use substitution multiple times.

Let l = time of the low speed pump to fill the pool, h = time of the high speed pump to fill the pool.
Assuming that the relationship is linear when using both the low speed pump and the high speed pump at the same time we get

l = h+3
h+l = 8

then solve.

I just tried that, but it didn't get the right answer (got 2.5 for h). I thought about it and the individual times for the pumps added together couldn't be 8, could they, because it'd take less time to fill the pool using two pumps, not both the times added together?

Edit: It's okay, I found the answer/working here: I need help with the working in a very hard math problem please? - Yahoo! Answers NZ
• Mar 10th 2013, 09:06 PM
Let the volume of the pool be V, and consider $v_l$ and $v_h$ be the speed of each pump (litres per hour) and $t_h$ be the time it takes to fill the pool with the high speed pump alone, and $t_l$ be the time it takes to fill the pool with the low speed pump alone
$v_h = \frac{V}{t_h}$
$v_l = \frac{V}{t_l} = \frac{V}{t_h+3}$
$v_{h+l} = \frac{V}{8} = \frac{V}{t_h} + \frac{V}{t_h+3}$ (they fill at the same rate, added together.)
Hence $\frac{1}{8} = \frac{1}{t_h} + \frac{1}{t_h+3}$ solve for $t_h$