An amusement park ride has an elevator that brings riders to the top of a tower. Riders step off the elevator onto a slide, which is a straight line from the top of the tower to level ground. The base of the slide is 400 feet from the base of the tower and the length of the slide is 500 ft. If the elevator rises at a rate of 10 feet per second, how many seconds does the elevator take to rise from the ground to the top of the slide?
Question
An amusement park ride has an elevator that brings riders to the top of a tower. Riders step off the elevator onto a slide, which is a straight line from the top of the tower to level ground. The base of the slide is 400 feet from the base of the tower and the length of the slide is 500 ft. If the elevator rises at a rate of 10 feet per second, how many seconds does the elevator take to rise from the ground to the top of the slide?
Solution
The problem describes a right triangle where the length of the slide is the hypotenuse, the height of the tower is one leg, and the distance from the base of the slide to the base of the tower is the other leg. This is a classic Pythagorean theorem problem, where a² + b² = c².
In this case, we know the length of the slide (c = 500 feet) and the distance from the base of the slide to the base of the tower (b = 400 feet). We can solve for the height of the tower (a) using the Pythagorean theorem:
a² + b² = c² a² + 400² = 500² a² = 500² - 400² a² = 250000 - 160000 a² = 90000 a = sqrt(90000) a = 300 feet
So, the height of the tower is 300 feet.
The elevator rises at a rate of 10 feet per second, so to find out how many seconds it takes for the elevator to rise from the ground to the top of the slide, we divide the height of the tower by the rate of the elevator:
Time = Distance / Rate Time = 300 feet / 10 feet per second Time = 30 seconds
So, it takes the elevator 30 seconds to rise from the ground to the top of the slide.
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