Question

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

Hint:

In speed-distance problems, the equation is usually written as: \(\text{Time}_{\text{slow}} - \text{Time}_{\text{fast}} = \text{Difference}\).

Answer 1

Step 1: Understanding the Concept:
We use the relationship \(\text{Time} = \text{Distance} / \text{Speed}\). The difference in time between the two trains is given as 1 hour.
Step 2: Key Formula or Approach:
Let speed of faster train = \(x\) km/hr. Then slower train = \((x-10)\) km/hr.
Step 3: Detailed Explanation:
1. Equation based on time: \[ \frac{200}{x-10} - \frac{200}{x} = 1 \] 2. Multiply by \(x(x-10)\): \[ 200x - 200(x-10) = x^2 - 10x \] \[ 200x - 200x + 2000 = x^2 - 10x \implies x^2 - 10x - 2000 = 0 \] 3. Factorize: \((x - 50)(x + 40) = 0\). 4. Speed cannot be negative, so \(x = 50\). 5. Faster train = 50 km/hr; Slower train = 40 km/hr.
Step 4: Final Answer:
Speeds are 50 km/hr and 40 km/hr.