Model 2 Train Vs Train in opposite direction Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Using Rule 3,

When a train crosses a telegraph post, it covers its own length.

Speed of first train

= $120/10$ = 12 m/sec.

Speed of second train

= $120/15$ = 8 m/sec.

Relative speed

= 12 + 8 = 20 m/sec.

Required time

= $\text"Total length of trains"/ \text"Relative speed"$

= ${2 × 120}/20$ = 12 seconds.

Answer: (a)

Using Rule 3,

Total length of trains

= 140 + 160 = 300 m.

Relative speed

= 60 + 40 = 100 kmph

= 100 × $5/18$ m/sec. or $250/9$ m/sec.

Time taken to cross each other

= $300/{250/9} = {300 × 9}/250 = 10.8$ sec.

Answer: (a)

Let the length of each train be x metres

Then, Speed of first train = $x/3$ m/sec

Speed of second train = $x/4$ m/sec

They are moving in opposite directions

Relaive speed = $x/3 + x/4$

= ${4x + 3x}/12 = {7x}/12$ m/sec.

Total length = x + x = 2 x m.

Time taken = ${2x}/{{7x}/12}$

= $24/7 = 3{3}/7$ sec.

Answer: (b)

Using Rule 3,

Let the speed of each train be x kmph.

Their relative speed

= x + x = 2x kmph.

Time taken

= $\text"Total length of trains"/\text"Relative Speed"$

= $12/{60 × 60} = {240 × {1/1000}}/{2x}$

= $1/300 = 120/{1000x}$

$x = {300 × 120}/1000$ = 36

The required speed = 36 kmph.

Answer: (d)

Let the trains meet after t hours

Then, 21t - 16t = 60

5t = 60 ⇒ t = 12 hours

Distance between A and B

= (16 + 21) × 12

= 37 × 12 = 444 miles

Here, a = 21, b = 16, d = 60

Distance between A and B

= $({a + b}/{a - b}) × d$

= $({21 + 16}/{21 - 16}) × 60$

= $37/5 × 60$ = 37 × 12 = 444 miles

Answer: (d)

Using Rule 3,

Let the length of each train be x metre.

Speed of first train = $x/18$ m/sec

Speed of second train = $x/12$ m/sec

When both trains cross each other, time taken

= ${2x}/{x/18 + x/12}$

= ${2x}/{{2x + 3x}/36} = {2x × 36}/{5x}$

= $72/5$ = 14.4 seconds