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questions for multiple precalculus and probability

1) Jack and Jill ran a 200 meter race. Jill ran the race in 25 seconds and won by 5 meters; that is Jack had run only 195 meters when Jill crossed the finish line. They decide to race again, but this time Jill starts 5 meters behind the starting line. Assuming that both runners run at the same pace as before, who will win the second race and by how many seconds?

2) Suppose you have a pipe with circumference 8 cm and length 20 cm and that 10 turns of a wire are wrapped around the pipe. What is the length of the wire?

3) It takes you 40 seconds to walk from the first (ground) floor of a building to the fourth floor. How long will it take to walk from the first floor to the eight floor (at the same pace, assuming all floors have the same height)?

4) Marlene rides her bicycle to her friend Johns house and returns home by the same route. Marlene rides her bike at constant speeds of 9 mph on level ground, 6 mph when going uphill and 18 mph when going downhill. If her total time riding was 1 hours, how far is to Johns house?

5) A standard 6-sided die is weighted so that the probabilities of rolling 2,3,4,5 or 6 are equal and the probability of rolling 1 is three times the probability of rolling 2. If the die is thrown twice, what is the probability that the sum of the numbers thrown will be 4?

6) A cone has an altitude of 15 cm and a radius of 3 cm. A right circular cylinder of radius r and height h is inscribed in the cone. Write h as a function of r.

7) If 2f(x)+f(1-x)=x^2, what is f(x)?

8) Two hundred stones are placed on the ground 3 feet apart, the first being 3 feet from a basket. The basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by one?

9) 52 Freshman were interviewed about the classes they were taking this semester.
20 said they were taking science classes.
19 said they were taking math.
21 said they were taking English.
6 said they were taking both science and math.
8 said they were taking both science and English.
6 said they were taking both math and English.
2 said they were taking all three classes.
How many students are not taking any math, science, or English?
How many students are taking exactly one of science, math, or English?

10) Leon, who is always in a hurry, walked up an escalator while it was moving, at the rate of one step per second, and reached the top in 28 steps. The next day, he climbed two steps per second (skipping none), also while it was moving, and reached the top in 40 steps. If the escalator had been stopped, how many steps did the escalator have from the bottom to the top?

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The solution provides detailed explanation how to solve precalculus and probability related questions.

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