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

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: (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: (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

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