A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ 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?

Given Data

• Train speed = 75 mph
• Tunnel length = 3.5 miles
• Train length = 0.25 mile
• Required: time from front entering to rear leaving the tunnel

Step 1: Total distance to clear the tunnel
Distance = tunnel length + train length = 3.5 + 0.25 = 3.75 miles

Step 2: Time = distance ÷ speed
Time (hours) = 3.75 ÷ 75 = 0.05 hConvert to minutes: 0.05 × 60 = 3 minutes

Checks & Common Pitfalls

• To clear a tunnel, add the train length to the tunnel length.
• Keep units consistent (miles and mph).

Final Answer
It takes 3 minutes for the train to pass completely.