Question 1028889: Suppose d is the distance traveled in miles and t is the time traveled in hours at a speed of 50 miles per hour. Is d directly proportional to t? If it is, enter the constant of proportionality. Otherwise, enter NO. Do not enter units.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
solve for time to get time = distance / rate.
this is the same as time = distance * (1/rate).
since the rate is constant, you can set k equal to 1/rate.
the formula becomes time = k * distance.
this means the time is directly proportional to the distance, as long as the speed is always the same.
for example:
you travel at 50 miles per hour for 2 hours.
your distance is 100 miles.
you travel at 50 miles per hour for 4 hours.
your distance is 200 miles.
you have a direct ratio of hours to miles.
2 hours is to 100 miles as 4 hours is to 200 miles.
2/100 = 4/200
cross multiply to get 2*200 = 4*100 which results in 400 = 400 which confirms the ratio is true.
the constant of proportionality is 1/50.
your equation is time = 1/50 * distance.
2 hours = 1/50 * 100 miles
4 hours = 1/50 * 200 miles
|
|
|
