SAT Math Multiple Choice Question 831: Answer and Explanation

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Question: 831

6. Cecilia leaves home for school on her bike at 9:05 AM, riding at an average speed of 10 miles per hour. Fifteen minutes later, her motherrealizes that Cecilia forgot to take her lunch. Cecilia's mother immediately getsinto her car and drives after Cecilia at an average speed of 25 miles per hour. Atwhat time will Cecilia's mom catch up to her?

  • A. 9:15 AM
  • B. 9:20 AM
  • C. 9:26 AM
  • D. 9:30 AM

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Strategic Advice: Almost all rate questions that involve distance and time can be solved using the formula Distance = rate × time. When you have two rates, consider organizing the information in a table.

Getting to the Answer: Think about each variable in the formula. You're given both rates (10 mph and 25 mph), so fill the rates in the table. When Cecilia's mother catches up to her, their distances will be the same (call the distance d). Because her mother leaves 15 minutes after Cecilia, call Cecilia's time t and her mother's time t - 15.

DistanceRateTime
Ceciliad10t
Cecilia's motherd25t - 15

Reading across each row of the table, the two equations are d = 10t and d = 25(t - 15). Set the two equations equal and solve for t:

Cecilia's mother will catch up at 9:05 AM + 25 minutes = 9:30 AM, choice (D).

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