Problem |
Solution |
1) A full can of paint contains 45 cubic inches of paint. It takes 1/3 of the can to paint one side of a door that is 6 feet 8 inches tall and 3 feet 4 inches wide. How thick is the paint on the door? Express your answer as a fraction of an inch reduced to lowest terms.
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- 1⁄3 of 45 = 15 cu. in.
- 6 ft 8 in = 80 inches; 3 ft 4 in = 40 inches.
- 80 x 40 x T = 15
- T = 15/3200 = 3/640 in
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2) The Telinos are tiling their bathroom. Part of the design will be a zigzag band all around the room. To create this they will need to cut white triangles and grey parallelograms from rectangle tiles. The rectangles have dimensions 4 cm by 12
cm as labeled. The triangles have height 7 cm. What is the perimeter of a parallelogram tile in centimeters? Round to the nearest centimeter.
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See the figure to the left for the missing dimensions.
- The missing dimension is the diagonal which is the hypotenuse of the triangle.
- Using the pythagorean theorem:
c =
√
(a 2 +
b 2)
- Plugging in our values:
c =
√
(4 2 +
7 2)
- c = 8.06 cm.
- So the perimeter of the parallelogram is
2(5) + 2(8.06) = 26.12 cm = 26 cm
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3) Shauna enters a bike race. She checks out the course one weekend and it takes her two hours to ride the course. If she rides at an average rate of 18 mph for the first third of the time, speeds up to 25 mph for the next 1/4 of the time, slows to 12 mph for the next 1/4 of the time and finishes with a
speed of 27 mph for the last 20 minutes of the course, what is her average rate in miles per hour? Express your answer to the nearest tenth of a mile per hour.
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Compute the distances for each leg and add:
- 18 mi x 40
min = 12 miles
60 min
- 25 mi x 30
min = 121⁄2 miles
60 min
- 12 mi x 30
min = 6 miles
60 min
- 27 mi x 20
min = 9 miles
60 min
- The course is 12 + 121⁄2 + 6 + 9 miles = 39.5 miles long.
- Average rate = 39.5 miles/2 hours = 19.8 mph
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