Sheila, Janice, and Karen, working together at the same rate, can complete
a job in 3 1/3 days. Working at the same rate, how much of the job could Janice
and Karen do in one day?

Let's solve the problem step by step.

1. **Total rate of work**:  
   Sheila, Janice, and Karen together can complete the job in \( 3 \frac{1}{3} \) days.  
   First, convert \( 3 \frac{1}{3} \) days to an improper fraction:  
   \[
   3 \frac{1}{3} = \frac{10}{3} \text{ days}
   \]  
   So, in one day, all three working together can complete:
   \[
   \text{Rate of work (all three together)} = \frac{1}{\frac{10}{3}} = \frac{3}{10} \text{ of the job per day}
   \]

2. **Individual rate of work**:  
   Since Sheila, Janice, and Karen work at the same rate, let's denote their individual rate as \( r \).  
   The total rate when they work together is:
   \[
   3r = \frac{3}{10}
   \]  
   Solving for \( r \):
   \[
   r = \frac{3}{10} \div 3 = \frac{1}{10} \text{ of the job per day}
   \]

3. **Rate of Janice and Karen together**:  
   Since Janice and Karen have the same rate, their combined rate is:
   \[
   \text{Rate of Janice and Karen} = 2r = 2 \times \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \text{ of the job per day}
   \]

Thus, **Janice and Karen together can complete \( \frac{1}{5} \) of the job in one day**.

Would you like any more details or have any questions?

Here are some related questions you might find interesting:
1. How much of the job could Sheila do alone in one day?
2. How long would it take Janice to complete the job alone?
3. If Sheila worked twice as fast as Janice and Karen, what would be the new rate of work for all three?
4. How long would it take Janice and Karen together to complete the entire job?
5. If a fourth person joined with the same work rate, how much of the job could they all do in one day?

**Tip:** When dealing with rates and time, always try to break down the problem by calculating individual rates and then combining them as needed.

Learn how to calculate the daily work rate of Janice and Karen in a collaborative job scenario. This problem involves understanding rates of work and converting mixed numbers to improper fractions. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation