SAT Math Multiple Choice Question 300: Answer and Explanation

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Question: 300

15. Water from rivers and streams is often unsafe to drink because of sediments and contaminants. One primitive way that water has been filtered in the past (and is still occasionally employed by avid campers and survivalists) is to use a charcoal filter, through which the water is allowed to trickle. Suppose three campers make three charcoal filters. The first two campers make their filters using water bottles, each of which can filter enough water for all three campers in 8 hours. The third filter is made from a two-liter soda bottle and can filter the same amount of water in 4 hours. How long will it take the three filters working together to filter enough water for all three campers?

  • A.
  • B. 1 hour
  • C.
  • D. 2 hours

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Strategic Advice: Determine the rate at which each filter cleans the water supply. Then add them together to get the combined rate.

Getting to the Answer: You're told that either of the two water-bottle-sized filters can filter the whole supply in 8 hours. This means one of these filters works at a rate of of the supply per hour. Likewise, the larger filter's rate is of the supply per hour. Add them all together, set them equal to (the rate for the entire task), and solve for t.

Therefore, working together, it would take all three filters 2 hours to filter the entire water supply.

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