# Thread: Rational functions - word problem

1. ## Rational functions - word problem

A group of students have volunteered for the student council car wash. Janet can wash a car in m minutes. Rodriguez can wash a car in m - 5 minutes, while Nick needs the same amount of time as Janet. If they all work together, they can wash a car in about 3.23 minutes. How long does Janet take to wash a car?

Succinct explanations in steps would be helpful. Thanks, guys.

2. Originally Posted by MHurricane
A group of students have volunteered for the student council car wash. Janet can wash a car in m minutes. Rodriguez can wash a car in m - 5 minutes, while Nick needs the same amount of time as Janet. If they all work together, they can wash a car in about 3.23 minutes. How long does Janet take to wash a car?

Succinct explanations in steps would be helpful. Thanks, guys.
work rates ...

janet ... (1 car)/(m minutes)

rod ... (1 car)/(m-5 minutes)

nick ... (1 car)/(m-5 minutes)

all three together complete the job in 3.23 minutes ...

$\displaystyle \left(\frac{1}{m} + \frac{1}{m-5} + \frac{1}{m}\right) \cdot (3.23) = 1$ car washed

solve the equation for $\displaystyle m$

3. Originally Posted by skeeter
work rates ...

janet ... (1 car)/(m minutes)

rod ... (1 car)/(m-5 minutes)

nick ... (1 car)/(m-5 minutes)

all three together complete the job in 3.23 minutes ...

$\displaystyle \left(\frac{1}{m} + \frac{1}{m-5} + \frac{1}{m}\right) \cdot (3.23) = 1$ car washed

solve the equation for $\displaystyle m$
I appreciate your efforts, however, you are wrong. Thanks, though. I got it.

4. Originally Posted by MHurricane
I appreciate your efforts, however, you are wrong. Thanks, though. I got it.
how do you figure?

I get m = 12 minutes

5. Originally Posted by skeeter
how do you figure?

I get m = 12 minutes
harharhar, you are right.