Train Speed Calculation Using Relative Speed

This problem involves two trains moving towards each other. We need to find the speed of the faster train using the concepts of relative speed, distance, and time.

Define Variables

• Let the speed of the train from B to A be s kmph.
• The train from A to B travels 35 kmph faster, so its speed is (s + 35) kmph. This is the faster train.
• The total distance between A and B is 3710 km.
• The time taken for the trains to meet is 35 hours.

Calculate Relative Speed

When two objects move towards each other, their relative speed is the sum of their individual speeds.

Relative Speed = Speed of train A + Speed of train B

Relative Speed = $(s + 35) + s = (2s + 35)$ kmph.

Apply Distance Formula

The relationship between distance, relative speed, and time is given by:

Distance = Relative Speed × Time

Substituting the known values:

$3710 = (2s + 35) \times 35$

Solve for the Speed (s)

1. Divide both sides by 35: $ \frac{3710}{35} = 2s + 35 $ $ 106 = 2s + 35 $
2. Subtract 35 from both sides: $ 106 - 35 = 2s $ $ 71 = 2s $
3. Divide by 2 to find $s$: $ s = \frac{71}{2} $ $ s = 35.5 \text{ kmph} $

This value, $s = 35.5$ kmph, is the speed of the slower train (the one travelling from B to A).

Find the Speed of the Faster Train

The speed of the faster train (from A to B) is $s + 35$ kmph.

Speed of Faster Train = $35.5 + 35$

Speed of Faster Train = $70.5$ kmph.

Conclusion

The speed of the faster train is 70.5 kmph.