Question

jasmine can clean her house in 6 hours while her roommate can clean the house in 5 hours. how long would it take them to clean the house if they work together? enter your answer in hours and rounded to two decimal places if needed. hours

Explanation:

Step1: Define work rates

Jasmine's rate: \( \frac{1}{6} \) house per hour (since she takes 6 hours to clean 1 house).
Roommate's rate: \( \frac{1}{5} \) house per hour (since she takes 5 hours to clean 1 house).

Step2: Combined work rate

When working together, their combined rate is the sum of their individual rates:
\( \frac{1}{6} + \frac{1}{5} = \frac{5 + 6}{30} = \frac{11}{30} \) house per hour.

Step3: Time to complete 1 house together

Let \( t \) be the time together. The work done is rate \( \times \) time, so:
\( \frac{11}{30} \times t = 1 \)
Solve for \( t \): \( t = \frac{30}{11} \approx 2.73 \) hours.

Answer:

\( 2.73 \)