Question

a train is traveling at a constant speed and traveled 67.6 miles in the last 1 1/2 hours. which equation shows the proportiomal relationship between the distance, d, and the time, t, that the train has traveld?

Answer 1

d = 45t

Explanation:

Define the variables:

• Let d = distance traveled (in miles)
• Let t = time (in hours)

`\large \boxed{\sf Distance=speed * time}`

Therefore, if the train traveled at a constant speed (k) then:

`\boxed{d = kt}`

where k is some constant to be found.

Given:

• d = 67.5 miles
• t = 1.5 hours

Substitute the given values into the formula and solve for k:

`\begin{aligned}d & = kt \\\implies 67.5 & = 1.5k \\k & = (67.5)/(1.5) \\k & = 45\end{aligned}`

Substitute the found value of k into the equation thus creating an equation that shows a proportional relationship:

`\large \boxed{d=45t}`