A train travelling at a speed of 75 mph enters a tunnel 3.5 miles long. The train is 5.5 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?


Question 2Answer

a.
8.2 min


b.
2.1 min


c.
7.2 min


d.
5.6 min

To solve this problem, we need to determine the total distance the train needs to travel to completely pass through the tunnel and then calculate the time taken to travel that distance.

### Step 1: Calculate the total distance.
- The tunnel is 3.5 miles long.
- The train itself is 5.5 miles long.

When the front of the train enters the tunnel, the rear of the train will still need to cover the length of both the tunnel and the train before it fully exits. Therefore, the total distance the train must travel is:

\[
\text{Total distance} = 3.5 \text{ miles (tunnel)} + 5.5 \text{ miles (train)} = 9 \text{ miles}.
\]

### Step 2: Calculate the time taken.
The train is traveling at a speed of 75 miles per hour. The formula to calculate time is:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}.
\]

Substituting the values:

\[
\text{Time} = \frac{9 \text{ miles}}{75 \text{ miles per hour}} = 0.12 \text{ hours}.
\]

### Step 3: Convert the time from hours to minutes.
Since there are 60 minutes in an hour:

\[
0.12 \text{ hours} \times 60 \text{ minutes per hour} = 7.2 \text{ minutes}.
\]

### Answer:
The correct answer is **(c) 7.2 minutes**.

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Would you like more details or have any questions?

Here are some related questions to expand your understanding:
1. How would the time change if the train were traveling at a different speed?
2. What if the tunnel were longer or shorter? How would that affect the time?
3. How is the formula for time derived from the speed and distance equations?
4. How would the problem change if the train's length were different?
5. How can we apply similar principles to solve problems involving boats, cars, or planes?

**Tip:** Always double-check unit conversions (e.g., hours to minutes) to avoid errors when solving time problems.

Learn how to calculate the time taken for a train to pass through a tunnel when given its speed and lengths of the train and tunnel. Detailed step-by-step solution with time conversion included.

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