A passenger train's speed is 60 mi/hr and a freight train's speed is 40 mi/hr.  The passenger train travels the same distance in 1.5 hr less time than the freight train.  How long does the freight train take to make the trip?

Let the time the freight train takes to travel the distance be denoted as \( t \) (in hours). Since the passenger train takes 1.5 hours less than the freight train, its travel time will be \( t - 1.5 \) hours.

We know that the distance traveled by both trains is the same. The distance formula is:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

For the freight train, the distance is:

\[
\text{Distance} = 40 \times t
\]

For the passenger train, the distance is:

\[
\text{Distance} = 60 \times (t - 1.5)
\]

Since both distances are equal, we set up the equation:

\[
40t = 60(t - 1.5)
\]

### Solving for \( t \):

First, distribute on the right-hand side:

\[
40t = 60t - 90
\]

Next, subtract \( 60t \) from both sides:

\[
40t - 60t = -90
\]

\[
-20t = -90
\]

Divide both sides by -20:

\[
t = \frac{90}{20} = 4.5 \text{ hours}
\]

Thus, the freight train takes **4.5 hours** to make the trip.

Would you like any further details on this problem?

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Here are 5 related questions to deepen understanding:

1. What is the total distance both trains traveled?
2. How long did the passenger train take to complete the trip?
3. What is the difference in the distances traveled by the two trains after 3 hours?
4. If the freight train’s speed was reduced by 10 mi/hr, how much longer would it take to travel the same distance?
5. How long would it take if both trains traveled at 50 mi/hr?

**Tip:** When solving problems with distances, use the same units (e.g., miles and hours) consistently to avoid mistakes.

A passenger train's speed is 60 mi/hr and a freight train's speed is 40 mi/hr. The passenger train travels the same distance in 1.5 hr less time than the freight train. How long does the freight train take to make the trip?

Learn how to solve a real-world problem involving two trains traveling at different speeds. The passenger train travels at 60 mi/hr and the freight train at 40 mi/hr, with the passenger train taking 1.5 hours less. Find out how long the freight train takes to complete the trip using algebraic methods and the formula Distance = Speed × Time.

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