Trent can deliver his newspapers in 20 minutes. It takes Lois 60 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Answer 1

To find out how long it would take Trent and Lois to deliver the newspapers when they work together, we can use their rates of work.

First, we calculate the rate of work for each person:

• Trent can deliver the newspapers in 20 minutes, so his rate is: \[ \text{Rate of Trent} = \frac{1 \text{ route}}{20 \text{ minutes}} = \frac{1}{20} \text{ routes per minute} \]

• Lois can deliver the newspapers in 60 minutes, so her rate is: \[ \text{Rate of Lois} = \frac{1 \text{ route}}{60 \text{ minutes}} = \frac{1}{60} \text{ routes per minute} \]

Next, we add their rates together to find their combined rate: \[ \text{Combined rate} = \text{Rate of Trent} + \text{Rate of Lois} = \frac{1}{20} + \frac{1}{60} \]

To add these fractions, we need a common denominator. The least common multiple of 20 and 60 is 60. We can express \(\frac{1}{20}\) with 60 as the denominator: \[ \frac{1}{20} = \frac{3}{60} \] So we can rewrite the combined rate as: \[ \text{Combined rate} = \frac{3}{60} + \frac{1}{60} = \frac{4}{60} = \frac{1}{15} \text{ routes per minute} \]

Now, we need to find the time it takes them to complete one route together. The time \(T\) taken for one route is the reciprocal of their combined rate: \[ T = \frac{1 \text{ route}}{\frac{1}{15} \text{ routes per minute}} = 15 \text{ minutes} \]

Thus, if Trent and Lois work together, it will take them 15 minutes to deliver the newspapers.

The final answer is: \[ \boxed{15 \text{ minutes}} \]