The speeds of two trains are in the ratio 5 : 3. If the first train covers 350…

Concept: When two quantities are given in a ratio, the ratio only fixes the proportion between them, not their actual values. Introduce a common multiplier x for the ratio parts, find x from one known actual value (using speed = distance ÷ time here), then scale the other ratio part by the same x to get its actual value.

Application:

1. Let the speeds of the first and second trains be 5x and 3x respectively, since their ratio is 5 : 3.

2. The first train covers 350 km in 2 hours, so its speed = 350 ÷ 2 = 175 km/h.

3. Since the first train's speed is 5x, set 5x = 175, which gives x = 35.

4. The second train's speed is 3x = 3 × 35 = 105 km/h.

Cross-check: 175 : 105 simplifies (dividing both by 35) to 5 : 3, matching the given ratio, so the second train's speed of 105 km/h is confirmed.