The question asks us to find the unit rate in tasks per hour, given:

$1 \frac{2}{5} \text{ tasks for } 2 \frac{1}{3} \text{ hours}$

Step 1: Convert Mixed Numbers to Improper Fractions

1. Convert $1 \frac{2}{5}$ tasks: $1 \frac{2}{5} = \frac{5 \times 1 + 2}{5} = \frac{7}{5} \text{ tasks}$

2. Convert $2 \frac{1}{3}$ hours: $2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3} \text{ hours}$

Step 2: Calculate the Unit Rate

The unit rate in tasks per hour is found by dividing the number of tasks by the time in hours:

$\text{Unit rate} = \frac{\frac{7}{5} \text{ tasks}}{\frac{7}{3} \text{ hours}} = \frac{7}{5} \times \frac{3}{7} = \frac{21}{35} = \frac{3}{5} \text{ tasks per hour}$

Answer

The unit rate is $\frac{3}{5}$ tasks per hour.

Would you like more details on the process?

Here are some related questions you might find helpful:

1. How do you simplify complex fractions?
2. What is a unit rate, and how is it different from a ratio?
3. How do you convert between mixed numbers and improper fractions?
4. What are common applications of unit rates in real life?
5. How can unit rates help in comparing efficiency?

Tip: When dividing by a fraction, remember that it’s the same as multiplying by the reciprocal!