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

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: (a)

Using Rule 3,

Total length of both trains = 250 metres

Let speed of second train =x kmph

Relative speed = (65 + x) kmph

= (65 + x) × $5/18$ m/sec

Time

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

6 = $250/{(65 + x) × 5/18$

$6 × 5/18 × (65 + x)$ = 250

65 + x = ${250 × 3}/5$

65 + x = 150

x = 150 - 65 = 85 kmph

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: (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

Answer: (a)

If two trains be moving in opposite directions at rate u and v kmph respectively,

then their relative speed = (u + v) kmph.

Further, if their length be x and y km. then time taken to cross each other

= ${x + y}/{u + v}$ hours.

Here, Total length = 160 + 140 = 300m.

Relative speed = (77 + 67) kmph

= 144 kmph = 144 × $5/18$ m/s or 40 m/sec.

Time = $300/40 = 7{1}/2$ Seconds

Answer: (b)

Let train A start from station A and B from station B.

Let the trains A and B meet after t hours.

Distance covered by train A in t hours = 50t

Distance covered by train B in t hours = 60t km

According to the question,

60t - 50t = 120

t = $120/10$ = 12 hours.

Distance AB = 50 × 12 + 60 × 12

= 600 + 720 = 1320 km

Here, a = 60, b = 50, d = 120

Distance between A and B = $({a + b}/{a - b}) × d$

= $({60 + 50}/{60 - 50}) × 120$

= $110/10 × 120$ = 1320 km