Question

Solve each problem. See Example 2. Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In 1/2 hr, the planes are 275 mi apart. What are their speeds?

Accepted Answer

Define variables for the speeds of the two planes. Let the speed of the San Francisco plane be $$x$$ mph. Since the San Diego plane flies 50 mph slower, its speed will be $$x - 50$$ mph. Express the distances each plane travels in terms of their speeds and the time traveled. Both planes travel for $$\frac{1}{2}$$ hour, so the distance traveled by the San Francisco plane is $$x 	imes \frac{1}{2} = \frac{x}{2}$$ miles, and the distance traveled by the San Diego plane is $$(x - 50) 	imes \frac{1}{2} = \frac{x - 50}{2}$$ miles. Since the planes are flying in opposite directions, the total distance between them after half an hour is the sum of the distances each has traveled. Set up the equation: $$\frac{x}{2} + \frac{x - 50}{2} = 275. $$Combine like terms on the left side of the equation to simplify it. This will give you an equation in terms of $$x$$ that you can solve. Solve the resulting linear equation for $$x to $$find the speed of the San Francisco plane. Then subtract 50 from $$x to $$find the speed of the San Diego plane.

Solve each problem. See Example 2. Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In 1/2 hr, the planes are 275 mi apart. What are their speeds?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Relative Distance and Speed

Setting Up Algebraic Equations

Solving Systems of Equations