You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.
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Question: Question: A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)?

 Option A: 18

 Option B: 36

 Option C: 60

 Option D: 96

 Option E: 112 minutes

Answer: Option E


Question: Question: If p/8 = r/2 and r = 0.75s, what is the ratio of p to r to s?

 Option A: 2 : 3 : 4

 Option B: 8 : 12 : 9

 Option C: 24 : 6 : 8

 Option D: 6 : 4 : 3

 Option E: 12 : 8 : 3

Answer: Option C


Question: Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?

 Option A: 7

 Option B: 8

 Option C: 6

 Option D: 9

 Option E: 5

Answer:
Option D