ratio problem

[mature student]

I am stuck with this problem:

Megan and Sam together take 12 minutes to wash a car. Washing the car by herself took Megan 21 minutes. How long would it take Sam to wash the car?

Any help or hint would be much appreciated

 

[pappus]

I am stuck with this problem:

Megan and Sam together take 12 minutes to wash a car. Washing the car by herself took Megan 21 minutes. How long would it take Sam to wash the car?

Any help or hint would be much appreciated

1. Let t denotes the time Sam needs to wash the car.

2. Then Megan washes \(\displaystyle \frac1{21}\) of the car in 1 minute

and Sam washes \(\displaystyle \frac1{t}\) of the car in 1 minute. That means: In one minute they will wash together \(\displaystyle
\left(\frac1{21} + \frac1t\right)\) of the car.

3. According to the text they work together for 12 minutes:

\(\displaystyle 12 \cdot \left(\frac1{21} + \frac1t\right) = 1\ (car)\)

Solve for t.

 

[mmm4444bot]

With these work-type word problems, it is often helpful to think in terms of the fractional amount of the task completed per unit of time.

That is what pappus did for step 2.