Question

Two trains are 100 km apart are traveling in the same direction if the speed of the faster train is 50 km/hr and the slower train is x km/hr and the faster train takes x/6 hours to overtake the slower train, then what can be the speed of the slower train?

1. 40 km/hr or 20 km/hr
2. 30 km/hr or 20 km/hr
3. 30 km/hr
4. 30 km/hr or 50 km/hr

Answer 1

Correct Answer - Option 2 : 30 km/hr or 20 km/hr

Given:

Distance between trains = 100 km

Speed of faster = 50 km/hr

Speed of slower train = x km/hr

Time taken to overtake = x/6 hour

Concept used:

When A and B travel in the same direction = Relative speed becomes A – B (i.e. Relative speed is difference of their individual speed when they travel in same direction)

When A and B travel towards each other = Relative speed becomes A + B (i.e. Relative speed is sum of their individual speed when they travel towards each other)

Time = Distance/Speed

Calculation:

Relative speed = (50 – x) km/hr

Time taken = Distance between them/Relative speed

⇒ x/6 = 100/(50 – x)

⇒ x × (50 – x) = 6 × 100

⇒ 50x – x² = 600

⇒ x² – 50x + 600 = 0

⇒ x² – 30x – 20x + 600 = 0

⇒ x × (x – 30) – 20 × (x – 30) = 0

⇒ (x - 20) × (x - 30) = 0

⇒ x = 30 and x = 20

There are two values of x which satisfy the given conditions.

∴ The speed of slower train can be 30 km/hr or 20 km/hr