Question

The distance traveled varies directly with the time spent in motion when speed is held constant. If d represents the distance traveled and t represents time, which equation would represent this variation? If you travel 150 miles in 4 hours, what is the constant of variation? If you continue traveling at a constant speed, how long will it take to travel 200 miles? Round to the nearest tenth of an hour. about hours\

Answer 1

D=kt

37.5

5.3 hours.

Answer 2

We have a direct variation. Distance, D, varies directly as time, t.
So D = Kt where K is the constant. In this case, speed. So D = Kt is our constant of variation.
If D = 150 miles and t = 4 hours
Then we have 150 = K (4)
K = 150/4 = 37.5. The constant of variation is 37.5.
If you keep traveling at a constant speed K = 37.5 and D = 200. We have
200 = 37.5 * t
t = 200/37.5 = 5.333 hours.