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

Answer:

d = 45t

Step-by-step explanation:

Define the variables:

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

$\large \boxed{\sf Distance=speed \times time}$

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:

$\begin{aligned}d & = kt \\\implies 67.5 & = 1.5k \\k & = \dfrac{67.5}{1.5} \\k & = 45\end{aligned}$

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

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