P, V and G had to paint three identical fences. On the

Question

P, V and G had to paint three identical fences. On the first day, only P turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m –4) hours. On the third day, V and G turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m?

a) 6
b) 8
c) 9
d) 10
e) 12

a) 6
b) 8
c) 9
d) 10
e) 12

nick1816 · Answer

\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}

m^2-8m-20=0

m=10

Chaman51 · Answer

\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}

m^2-8m-20=0

m=10

Could you provide more detail on how you resolve this equation?

Thanks

KarishmaB · Answer

Since P takes m hrs to complete one fence, his rate of work = 1/m fence/hr = p
P, V and G take (m - 4) hrs to complete one fence so their rate of work = 1/(m - 4) fence/hr = p + v + g
V and G take (m + 5) hrs to complete one fence so their rate of work = 1/(m + 5) = v + g

1/m + 1/(m+5) = 1/(m - 4)

Now just try to plug in the options to see which value of m works. 
Note that m = 6 gives 11 in the second denominator on left hand side. It is a big prime number and seeing that on right hand side, we will have 1/2, m = 6 will not work. Same logic works for 8 and 9 too.

The first option you should actually try is m = 10 which works.

Answer (D)

nick1816 · Answer

Chaman51

\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}

\frac{m+5+m}{m(m+5)}=\frac{1}{m-4}

\frac{2m+5}{m^2+5m}=\frac{1}{m-4}

(2m+5)(m-4)=m^2+5m

2m^2-3m-20=m^2+5m

m^2-8m-20=0

m^2-10m+2m-20=0

(m-10)(m+2)=0

stne · Answer

Hi  Chaman51 ,

If you arrive at an equation that has only one variable, and the answer choices give you values for that variable. You could simply try substituting the values from the answer choices.

In this question, the equation: 
 \frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}  will only be satisfied by m=10

Hope this helps.

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