daviddaviddavid wrote:
fast pump takes x hour
Slow pump takes 1.5x hour
1/x + 1/1.5x = 1/4
1/x = 1/4 - 1/1.5x
1/x = (1.5x - 4)/6x
6x = 1.5x^2 - 4x
10x = 1.5x^2
10 = 1.5x
x = 10/1.5 --> stop here during practice exam because it seems strange and you have a serious lack of confidence
x = 20/3
could someone confirm please ??
Quote:
EMPOWERgmatRichCQuote:
Salvetor fast pump takes x hour
Slow pump takes 1.5x hour
so
1/x+1/1.5x = 1/4
> (1.5+1)/1.5x = 1/4
> 2.5/1.5x = 1/4
> 1.5 x = 10
>x = 10/1.5
>x = 20/3
Somebody confirm whether this is a right approach to do this type of problem or not. Thanks
Hi Salvetor,
Yes, your approach is correct. In 'Work' questions, there are usually several different ways to organize the given information, but they all end up involving a ratio at some point.
daviddaviddavid , your approach is almost identical to Salvetor's. You just used slightly different algebra.
I did the algebra your way one time and a second time using a fusion of your and Salvetor's approach.
He added. You subtracted. You used a different LCM or this shortcut: \(\frac{a}{b} + \frac{c}{d} = \frac{(da + bc)}{bd}\). So I fused by adding, as Salvetor did, and by using your LCM. Both your method and fusion method gave me the correct answer.
I think you should swagger a bit in your head.
You took the way four people here asked about, which also seems to me to be the most direct way.
Here's the math done in a way that fuses Salvetor's method and yours:
\(\frac{1}{x} + \frac{1}{1.5x} = \frac{1}{4}\)
\(\frac{(1.5x + x)}{1.5x^2} = \frac{1}{4}\)
\(4 (1.5x + x) = 1.5 x^2\)
\(4 (2.5x) = 1.5 x^2\)
\(10 x = 1.5 x^2\), divide by x (we're allowed b/c we know x is not 0):
\(10 = 1.5x\)
Get rid of the decimal in the denominator. Multiply by sides by 10 →
\(100=15x\)
\(x=\frac{100}{15}=\frac{20}{3}\)
Or convert
1.5 in the denominator to the fraction \(\frac{3}{2}\)
Thus:
\(x = \frac{10}{1.5}=\frac{10}{\frac{3}{2}}=\)
\((10*\frac{2}{3})=\frac{20}{3}\)
Decimals in denominators look strange to me, too. Make a little rule: if decimal in denominator isn't in answer choices, either multiply the fraction by 10/10 or 100/100 etc., or convert the decimal to a fraction.
You just got stuck on the part where multiplying your answer by 2 would match one of the choices. Very frustrating. And common. Not to worry. :wink:
Hope it helps.
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