Problem Solving

Question

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

Suppose it takes about 3 seconds to hear the echo. How far away is the canyon wall, in feet??

Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n??

Answer 1

750 mph = 750 miles/60 minutes = 75/6 = 75/360seconds = 15/72 = 5/24 miles per second

in 3 seconds the sound traveled 3(5/24) miles = 5/8 mile

that's double the distance to the canyon wall. It's 5/16 mile away. 1 mile = 5280 feet

5280(5/16) = 1,650 feet

750x5280/3600 = 1100 feet if the echo took 2 seconds. 550 feet for 1 second, 550x3 = 1650 for 3 second echo.

in n seconds then the distance to the canyon wall would be 550n feet

n(5/48) = 5n/48 miles = 5280(5n/48) = 550n feet