Question

A train running at uniform speed crosses 600m and 300m long two bridges in 2 minutes and 80 seconds respectively .what is the speed of the train?

Answer 1

First of all we have to find out length of train .
Let length of train is L

Now, time taken to cross first bridge of 600 m length is 2 min
e.g., speed of train = distance/time
= (Length of train + length of bridge)/time
= (L + 600)/2 × 60
= (L + 600)/120

Again, time taken to cross the 2nd bridge of length 300m is 80 second
e.g., speed of train = distance/time
= (L + 300)/80

LET SPEED OF TRAIN IS CONSTANT.
so, (L + 600)/120 = (L + 300)/80
⇒ (L + 600)/3 = (L + 300)/2
⇒ 2L + 1200 = 3L + 900
⇒300 = L
Hence, length of train is 300 m

Now, speed of train = (L + 600)/120
= (300 + 600)/120
= 900/120
= 90/12
= 30/4 = 7.25 m/s

Answer 2

Hello Dear.

Here is the answer---

Let the Length of the train be x m.

Given ⇒
In First Case,
Length of the First Bridge = 600 m.
Distance covered by the Train = Length of the train + Length of the first Bridge
= (x + 600)m.
Time taken to cross the Bridge = 2 min.
= 2 × 60
= 120 seconds.

∵ Speed = Distance/Time
∴ Speed of the train = (x + 600)/120 m/s. -----eq(i)


In Second Case,

Length of the Bridge = 300 m.
Total Distance covered by the train = Length of the Train + Length of the Bridge.
= (x + 300)m.
Time taken to cross the bridge = 80 seconds.

∴ Speed of the train = (x + 300)/80 m/s. -----eq(ii)


Assuming the Speed of the train is constant,

        ∴ eq(i) = eq(ii)
(x + 600)/120 = (x + 300)80
2x + 1200 = 3x + 900
3x - 2x = 1200 - 900
 x = 300 m.

∴ Length of the train is 300 m.

Now, For the Speed of the train,

Using the eq(ii),

Speed of the train = (x + 300)/80
 = (300 + 300)/80
 = 600/80
 = 60/8
 = 15/2
 = 7.5 m/s.

∴ Speed of the train is 7.5 m/s.


Hope it helps.