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 4 seconds to hear the echo. How far away is the canyon wall, in feet?

 feet

Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?

   feet

Answer 1

750 miles per hour = 750 mi./1 hr. = 750 mi./60 min. = 75 mi./6 min. = 75 mi/360 sec.

= 25mi/120 sec. = 5 mi./24 sec. = 5/6 mi./4 sec. The canyon wall is 5/6 of a mile. A mile = 4x440 yards = 4x440x3 feet. 5/6 of a mile = (5/6)x4x440x3 feet =5280 x 5/6 = 26400/6 = 4,400 feet

For n seconds

sound travels at 5/6 miles per 4 seconds or 5/24 miles per second

in n seconds, sound travels 5n/24 miles = (5n/24)(5,280) feet in n seconds

= 1100n feet in n seconds

in 4 seconds that's 1100(4) = 4400 feet