Math

1. In order to collect data on the signal strengths in a neighborhood, Briana must drive from house to house and take readings. She has a graduate student, Henry, to assist her in the task. Briana figures it would take her 12 hours to complete the task if working alone, and that it would take Henry 18 hours if he were to complete the task by himself.

How long will it take Briana and Henry if they complete the task together?

2. Briana can collect data from 5 more houses per hour than Henry. It took Briana two hours less to collect data from 120 houses than it took Henry to collect data from the same number of houses.
3. Joe is the owner and CEO of Pinecrest Enterprises, a real estate development company in Boise, Idaho. The company has taken on a new development project outside of town, and Joe wants to drive out to survey the proposed development site. The site is 30 miles away from Joe’s office. Setting a good example, Joe drives the speed limit of 45 miles per hour to the development site and back.
4. The development site consists of a rectangular plot of land, with a smaller rectangle set aside as National Forest land (which is not part of the site). Driving north along the eastern edge of the site, Joe uses the odometer in his truck to determine the length of the forest is 1.2 miles, and the remaining length of the site is 2.0 miles. He also knows the width of the forest is one mile less than the width of the southern portion of the site. (See the figure below.) The total area of the site excluding the forest is 16 square miles.
What is the width, x, of region 2, as shown in the picture above?

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  1. #1

    1/12 + 1/18 = 1/x

    Now, what do you think about the other parts? You must have some ideas about at least some of them.

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