# Tutor profile: Elizabeth S.

## Questions

### Subject: Geometry

Barbara needs to go one block east and one block south. If she cuts through the park and heads directly for her final destination, along the shortest path possible, how many feet less will she walk than if she were required to walk one block east and then one block north? One block = 100 feet.

If Barbara walks one block south and then one block east, she will walk 100 ft + 100 ft or 200 ft total. If she walks directly to the other corner, she will follow the hypotenuse of a right triangle. We know that if the two sides of a triangle adjacent to the corner are the same length, then the angles of the triangle are 90, 45, 45. We have a few ways of establishing the length of the hypotenuse of the triangle. We know that a^2 + b^2 = c^2. In this case, a = 100, b = 100 so 100^2 + 100^2 = c^2 = 20,000. To get rid of the squared on the c, take the square root of both sides. Square root of 20,000 = 141 ft, which is 41 feet longer than 100 ft.

### Subject: Basic Math

A woman regularly pays someone to mow her lawn and pays them $1 per square foot. If she decides to build a pool in her backyard, how much money will she save? Her yard is originally 100 feet by 100 feet. Her pool will have a circumference of 20* pi.

In this example, the money that she saves will equal the area of the pool times $1 per square foot. The original area of the pool is irrelevant. We can find the area of the pool by finding the radius of the pool. We know that circumference of a circle is 2 * pi * radius. This would make the radius 10 ft. We also know that the area of a circle is calculated as pi * radius^2 or pi * r * r. pi* 10 * 10 = 3.14159 * 10 * 10 = 314 square feet. If it costs $1 per square foot, she is saving $314.

### Subject: Algebra

Two students have been given the objective to finish writing a paper that is 1,260 words long. Student A sets a goal to write 300 words per day. Student B sets a goal to write 200 words per day. How much sooner must student B begin writing if both are to finish at the same time?Present your answer in days and hours.

Let's say: Student A requires x number of days to complete the assignment and Student B requires y number of days. The number of days required to complete the assignment is the words per day times the number of days. In other words, for student A: 300*x = 1,260 and for student B: 200*y-1,260. We can solve for both x and y by dividing the right side of the equation by the left. x = 1,260/300 = 4.2 days y = 1,260/200 = 6.3 days This means that student B took 2.1 days longer than student A (6.3-4.2=2.1). Don't forget that the question asked for days and hours. How many hours are in 0.1 days? If 1 day = 24 hours, then 0.1 days = 2.4 hours. The final answer is two days and 2.4 hours.

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