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?

Step 1: Understand the problem

• Speed of the train = 75 mph
• Length of the tunnel = 3.5 miles
• Length of the train = 0.25 miles
• To completely pass the tunnel, the train must cover: 3.5 + 0.25 = 3.75 miles

Step 2: Use the formula: Time = Distance / Speed

Total distance to be covered = 3.75 miles  
Speed = 75 miles/hour  

Time = 3.75 / 75 = 0.05 hours

Step 3: Convert time to minutes

0.05 hours × 60 minutes/hour = 3 minutes

Answer: The train takes 3 minutes to pass completely through the tunnel.

This question checks your understanding of relative distance when a train passes completely through a tunnel. The key idea is that the train must travel a distance equal to its own length plus the length of the tunnel. Converting units between miles, hours, and minutes is crucial for such real-life application problems.