Lesson A train passing through a tunnel

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A train passing through a tunnel

In this lesson you will find Travel and Distance problems on a train passing through a tunnel.

Problem 1

A train which has a length of 1%2F5

mile is traveling at a speed of 36 mph.
It enters a tunnel 1 mile long. How long does it take the train to pass through the tunnel from the moment the front enters the tunnel to the moment the rear leaves it?

Solution

The train should cover the distance

miles to pass through the tunnel from the moment the front enters the tunnel to the moment the rear leaves it.
Since the train has the speed 36 mph = 36%2F3600

= 0.01

, it will take %28%286%2F5%29%29%2F0.01

= 120 seconds = 2 minutes to pass through the tunnel.

Answer. 120 seconds, or 2 minutes.

Problem 2

A train 300 meters long is running with a speed of 45 km%2Fh

. The train crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?

Solution

According to the condition, the train covers 500 meters (its own length) plus the tunnel length in 1 minute.
Since the speed of the train is 54 km%2Fh

, it makes 45%2F60

= 750 meters in 1 minute. Hence, the tunnel length is 750-300 = 450 meters.

Answer. The length of the tunnel is 450 meters.

Problem 3

A train which has a length of d units is traveling at a speed v units per second.
It enters a tunnel of L units long. How long does it take the train to pass through the tunnel from the moment the front enters the tunnel to the moment the rear leaves it?
Solve the problem analytically (get the general formula).

Solution

The train should cover the distance (L + d) to pass through the tunnel from the moment the front enters to the moment the rear leaves. Since the train has the speed v units%2Fs

, it will take %28L%2Bd%29%2Fv

seconds to pass through the tunnel.

Answer. t = %28L%2Bd%29%2Fv

.

Travel and Distance problems on a train passing through a tunnel are twins of Travel and Distance problems on a train passing a platform (see the lesson
A train passing a plafrorm in this site).

Problem 4

A train which has a length of 90 meters, is traveling at a speed of 36 kilometers per hour.
It passes a platform 120 meters long. How long does it take the train to pass the platform from the moment the front of the train comes up to the closest end
of the platform to the moment the rear of the train comes comes up to the other end of the platform?

Solution

The train should cover the distance 120 meters (the length of the platform) plus 90 meters (its own length) = 210 meters to pass the platform from the moment
the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform.

Since the train has the speed 36 km%2Fh

= 10

, it will take 210%2F10

= 21 seconds to pass the platform.

Answer. 21 seconds.

My other lessons on Travel and Distance problems in this site are

- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
- Using fractions to solve Travel problems

- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Unpowered raft floating downstream along a river
- Selected problems from the archive on the boat floating Upstream and Downstream
- Selected problems from the archive on a plane flying with and against the wind

- Selected Travel and Distance problems from the archive

- Had a car move faster it would arrive sooner
- How far do you live from school?

- One unusual Travel problem
- Another unusual Travel problem (Arnold's problem on two walking old women)

- Travel problem on a messenger moving back and forth along the marching army's column
- A person walking along the street and buses traveling in the same and opposite directions

    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed

    - Clock problems
    - Advanced clock problems
    - Problems on bodies moving on a circle

    - A train passing a telegraph post and passing a bridge
    - A train passing a platform
    - A light-rail train passing a walking person
    - A train passing another train

    - A man crossing a bridge and a train coming from behind
    - A rower going on a river who missed the bottle of whiskey under a bridge
    - Non-traditional Travel and Distance problems

    - The distance covered by a free falling body during last second of the fall

    - The Doppler Shift

    - Entertainment Travel and Distance problems
    - OVERVIEW of lessons on Travel and Distance

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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