If Joan shovels a driveway in 50 minutes and Mary in 20 minutes, how long will it take them together?

• A. 12
• B. 13
• C. 14
• D. 15

Answer: (C)

To determine how long it will take Joan and Mary to shovel the driveway together, we can use the concept of rates of work.

First, we need to establish the rates at which Joan and Mary can shovel the driveway. Joan completes the task in 50 minutes, meaning her rate of work is ( \frac{1}{50} ) of the driveway per minute. Similarly, Mary finishes in 20 minutes, which gives her a rate of ( \frac{1}{20} ) of the driveway per minute.

To find their combined rate of work, we simply add their individual rates:

[

\text{Combined Rate} = \frac{1}{50} + \frac{1}{20}

]

To add these fractions, we need a common denominator. The least common multiple of 50 and 20 is 100. Therefore, we can rewrite the rates as follows:

[

\frac{1}{50} = \frac{2}{100}

]

[

\frac{1}{20} = \frac{5}{100}

]

Now, we can add the two fractions:

[

\text{Combined Rate} = \frac{2}{100} + \frac{5