My open math question 9

Question

sound travels about 750 miles per hour. if you stand in a canyon and sound a horn, you will hear an echo.

1. suppose it takes 1.5 seconds to hear an echo how far away is the canyon wall, in feet?
2. suppose it takes n seconds to hear that echo. how far away is the canyon wall, in terms of n.

Answer 1

750 miles per hour. You hear an echo in 1.5 seconds

750 mph = 750 miles per 60x60 seconds

= 750/3600 mps

= 75/360 mps

= 15/72 miles per one second

in 1 1/2 seconds the sound traveled 1.5(15)/72 miles

= 22.5/72 miles

= .3125 mile

1 mile = 5280 feet

5280 x 0.3125 = 1650 feet for the sound to go to the canyon wall and back

divide by two for the distance one way:

1650/2

= 825 feet to the canyon wall

in n seconds

5280/2 x (15/72)n

= 550n feet in n seconds

550(1.5) = 825 feet