**Find the Time Taken by a Train to Cross a Bridge or Tunnel :**

In this section, we will learn how to find the time taken by a train to cross a bridge or tunnel.

Time taken by a train of length l meters to pass a standing object of length b meters is the time taken by the train to cover (l + b) meters.

The relationship between distance, speed and time.

Time = Distance / Speed

Speed = Distance / Time

Distance = Time ⋅ Speed

To convert minutes into hour, we should divide the given minutes by 60.

- If we want to convert the speed from km/hr to m/sec, we should multiply the speed by 5/18.
- If we want to convert the speed from m/sec to km/hr, we should multiply the speed by 18/5.

**Example 1 :**

A train is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

**Solution :**

Standing object is railway platform of length 165 meters.

Moving object is train of length 110 meters and running at the speed of 132 km/hr.

Converting the speed from km/hr to m/sec

= 132 ⋅ (5/18)

= 22 ⋅ (5/3)

= (110/3) m/sec

Distance to be covered = 110 + 165

= 275 m

Time = distance / speed

= 275 / (110/3)

= 275 ⋅ (3/110)

= 7.5 seconds

So, the train of length 100 m long is taking 7.5 seconds to cross the railway platform 165 meters long.

**Example 2 : **

How long does a train 110 meters long running at the speed of 72 km/hr take to cross a bridge 132 meters in length ?

**Solution :**

Standing object is bridge of length 132 meters.

Moving object is train of length 110 meters.

Distance to be covered = 132 + 110

= 242 meters

Speed of the train = 72 km/hr

Speed in m/sec = 72 ⋅ (5/18)

= 20 m/sec

Time = Distance / Speed

= 242 / 20

= 12.1 seconds

So, the train of length 132 m is taking 12.1 seconds crosses the bridge of length 110 m.

**Example 3 :**

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.

**Solution :**

Let l and x be the length and speed of the train respectively.

The train of length l meters crosses a railway bridge of length 180 m in 20 seconds.

Time = Distance / Speed

20 = (l + 180) / x

x = (l + 180)/20 -----(1)

The train of length l meters crosses a man in 8 seconds.

8 = l / x

x = l / 8 -----(2)

(1) = (2)

(l + 180)/20 = l / 8

8(l + 180) = 20l

20l - 8l = 1440

12l = 1440

l = 1440/12

l = 120

By applying the value of l in (2), we get

x = 120/8

x = 15 m/sec

x = 15 (18/5)

x = 54 km/hr

Hence the length of the train is 120 m and speed is 54 km/hr.

After having gone through the stuff given above, we hope that the students would have understood how to find the time taken by a train to pass a man.

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**