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.

   Hint (a):

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

   More Help (a):

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

2. Solve using $d = rt$.

   Hint (b):

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

   More Help (b):

   $90=r \cdot 1.5$

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

   $60=r$

   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?

   Answer (c):

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