Question

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Accepted Answer

Let the distance between Denver and Minneapolis be $$d$$ miles. Since the return trip covers the same distance, both trips are $$d$$ miles each. Write expressions for the time taken for each leg of the trip using the formula $$	ext{time} = \frac{	ext{distance}}{	ext{speed}}. $$For the trip to Minneapolis, time is $$\frac{d}{50}$$ hours, and for the return trip, time is $$\frac{d}{55}$$ hours. Set up an equation for the total travel time by adding the two times and equating to 32 hours: $$\frac{d}{50} + \frac{d}{55} = 32. $$Find a common denominator for the fractions on the left side, which is $$50 	imes 55 = 2750$$, and rewrite the equation as $$\frac{55d}{2750} + \frac{50d}{2750} = 32. $$Combine the fractions to get $$\frac{105d}{2750} = 32$$, then solve for $$d by $$multiplying both sides by 2750 and dividing by 105: $$d = \frac{32 	imes 2750}{105}. $$This will give the distance between the two cities.

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Distance-Speed-Time Relationship

Average Speed and Different Routes

Setting Up and Solving Algebraic Equations