Questions: Leeson can proofread a newspaper copy in 4 hrs. If Ryan proofreads the same newspaper copy, it takes 3 hrs. How long would it take if they worked together? t= hrs - mins

Solution Steps

To find out how long it would take for Leeson and Ryan to proofread the newspaper copy together, we can use the concept of work rates. Leeson's work rate is 1/4 of the newspaper per hour, and Ryan's work rate is 1/3 of the newspaper per hour. By adding their work rates, we can find their combined work rate and then calculate the time it takes for them to complete the task together.

Leeson's work rate is given by: \[ \text{Leeson Rate} = \frac{1}{4} \text{ newspapers per hour} \] Ryan's work rate is: \[ \text{Ryan Rate} = \frac{1}{3} \text{ newspapers per hour} \]

The combined work rate when both work together is: \[ \text{Combined Rate} = \text{Leeson Rate} + \text{Ryan Rate} = \frac{1}{4} + \frac{1}{3} \] To add these fractions, we find a common denominator: \[ \text{Combined Rate} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \text{ newspapers per hour} \]

The time taken to complete one newspaper together is the reciprocal of their combined work rate: \[ t = \frac{1}{\text{Combined Rate}} = \frac{1}{\frac{7}{12}} = \frac{12}{7} \text{ hours} \] Converting this to hours and minutes: \[ t \approx 1.7143 \text{ hours} \quad \text{(which is } 1 \text{ hour and } 0.7143 \text{ hours)} \] Calculating the minutes: \[ 0.7143 \times 60 \approx 42.8571 \text{ minutes} \approx 43 \text{ minutes} \]

Final Answer