### Home > INT1 > Chapter 6 > Lesson 6.3.1 > Problem6-88

6-88.

A train traveled $90$ miles in $1.5$ hours. At the same rate how long will it take the train to travel $330$ miles.

1. Use proportions to solve and show your work with units.

$\frac{\text{?? miles}}{\text{?? hours}}=\frac{\text{?? miles}}{\text{?? hours}}$

$\frac{\text{90 miles}}{\text{1.5 hours}}=\frac{\text{330 miles}}{\textit{x}\text{ hours}}$ Now finish solving this proportion.

2. Solve using $d = rt$.

Since $90$ miles is the distance ($d$) and $1.5$ hours is the time ($t$), substitute in and solve for the rate ($r$).

$90=r \cdot 1.5$

$\frac{90}{1.5}=r$

$60=r$

Now use your rate of $\frac{60 \text{ miles}}{\text{hour}}$ to solve for time when the distance is $330$ miles.

3. Did you get the same solution?

Yes, both methods resulted in an answer of $5.5$ hours to travel the $330$ miles.