# SAT Math Multiple Choice Question 473: Answer and Explanation

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**Question: 473**

**8.** A freight train operator knows that on a 200-mile trip, if the freight cars are not fully loaded, she can save 1 hour of travel time by increasing her normal speed by 10 miles per hour. What is her normal speed in miles per hour?

- A. 40
- B. 45
- C. 55
- D. 60

**Correct Answer:** A

**Explanation:**

A

Difficulty: Medium

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

Strategic Advice: When a question concerns distance, rate, and time, organizing the information in a table is usually very helpful.

Getting to the Answer: Use the equation Distance = rate × time.

Distance | Rate | Time | |

Normal Trip | 200 | r | t |

Faster Trip | 200 | r + 10 | t – 1 |

Now, set up a system of equations: 200 = rt and 200 = (r + 10)(t – 1). Solve the system by solving the first equation for r and substituting the result into the second equation; the first equation is Tip: Go ahead and FOIL the factors in the second equation before substituting the value of r.

Now, factor out a 10, find a common denominator, and you'll wind up with a fairly nice quadratic equation to solve.

The two solutions are t = 5 and t = –4. Time can't be negative, so t = 5. Substitute this back into the first equation (because the question asks about her original speed) and solve for r. Her normal speed is miles per hour.