Option 4 : 315 mtere and 525 metre

Given:

The speed of train A = 60 km/hr

The speed of train B = 66 km/hr

Time = 24 seconds

Formula used:

Distance = Speed × Time

Time = Distance/Speed

When two bodies move in opposite direction,

Relative Speed = Sum of Speeds

Concept used:

To convert a speed from km/h to m/s, we multiply it by 5/18

Calculation:

Relative speed = (60 + 66) km/hr = 126 km/hr = [126 × (5/18)] = 7 × 5 = 35 m/s

Let the length of train B be x m,

Then, the length of train A be 3x/5 m

According to the question; we get,

Length of both train (distance) = Speed × Time

⇒ (x + 3x/5) = 35 × 24

⇒ 8x/5 = 35 × 24

⇒ x = 35 × 15 = 525 metre

The length of train A be 3x/5 m = [(3/5) × 525] = 315 metre

∴ The length (in m) of both train Is 315 metre and 525 metre respectively.

__Additional Information__

** Distance covered = Speed × Time**

- Units of Time, Speed and Distance
- The basic unit of time is a second, which could also be expressed in other units such as minutes (min) and hours (hr).
- The basic unit of speed is meter per second m/s, which could also be expressed in other units such as m/min or km/h.
- The basic unit of distance meter (m), which could also be expressed in other units such as kilometre (km).
- To convert a speed given in m/s into a speed in km/h, multiply with 18/5.
- To convert a speed given in km/h into a speed in m/s, multiply with 5/18.
- 1 km = 1000 m
- 1 min = 60 sec.

Relative speed

- Consider two bodies moving at speeds u and v.
- 1. When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds,
- (u – v) if u > v
- (v – u) if v > u.
- 2. When they are moving in the opposite directions, the relative speed between the two bodies is the sum of their speeds,
- (u + v).