Solving the Time Needed for A & B to Complete a Job Alone

[paulmdrdo1]

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.

 

[soroban]

Hello, paulmdrdo!

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?

Are you sure you know what "rate of work" means?

You have: A's rate of work is $$22.$$
What does that mean?

Does it take 22 hours for A to do the job?
Does he get $22 per hour?

Check the original question.
And note that you didn't answer it.

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.
. So A takes twice as long?

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

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.

Look at what you wrote.

You said A takes twice as long as B.