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#### paulmdrdo

##### Active member

- May 13, 2013

- 386

1. A’s rate of doing work is three times that of B. On a given day A and B work together for 4 hours; then B is called away and A finishes the rest of the job in 2 hours. How long would it take B to do the complete job alone?

if I let x = B's rate of work and 3x = A's rate of work, I'll have this equation,

$\displaystyle 4\left(\frac{1}{x}+\frac{1}{3x}\right)+2\frac{1}{x}=1$

then, $x=7\frac{1}{3}$ and $3x=22$ is this correct?

2. A and B working together can complete a job in 6 days. A works twice as fast as B. How

many days would it take each of them, working alone, to complete the job?

let x = required time for B to finish a job alone, 2x = required time for A to finish a job alone

$\displaystyle 6\left(\frac{1}{x}+\frac{1}{2x}\right)=1$

the answer is x = 9 days for B, and 2(9)= 18 days for A.

but this doesn't make sense. if A is twice as fast as B it will take A lesser time to complete a job than B.

please help.

if I let x = B's rate of work and 3x = A's rate of work, I'll have this equation,

$\displaystyle 4\left(\frac{1}{x}+\frac{1}{3x}\right)+2\frac{1}{x}=1$

then, $x=7\frac{1}{3}$ and $3x=22$ is this correct?

2. A and B working together can complete a job in 6 days. A works twice as fast as B. How

many days would it take each of them, working alone, to complete the job?

let x = required time for B to finish a job alone, 2x = required time for A to finish a job alone

$\displaystyle 6\left(\frac{1}{x}+\frac{1}{2x}\right)=1$

the answer is x = 9 days for B, and 2(9)= 18 days for A.

but this doesn't make sense. if A is twice as fast as B it will take A lesser time to complete a job than B.

please help.

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