SOLUTION: 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 pr

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

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