Question

If a train runs at 50 km/hr, it reaches 60 minutes earlier than its schedule time at its destination but if it runs at 8.33 m/s it reaches at its destination 300 minutes late, find the correct time for the train to complete its journey.

• A. 10 hours
• B. 6.5 hours
• C. 7.44 hours
• D. 13.3 hours

Hint:

In speed-distance-time problems with two scenarios, always set up equations where the constant quantity (usually distance) is isolated. This allows you to equate the variable expressions and solve for the unknown.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We have two scenarios for a train journey with different speeds and corresponding deviations from the scheduled time. We need to find the scheduled time of the journey. The distance is constant in both scenarios. 
Step 2: Key Formula or Approach: 
The fundamental relationship is Distance = Speed \( \times \) Time. We will set up two equations based on the two scenarios and solve them simultaneously. 
Step 3: Detailed Explanation: 
Let the distance be \(D\) km and the scheduled time be \(T\) hours. 
Unit Conversion: First, convert all units to be consistent (km and hours). Speed in the second case is 8.33 m/s. Let's convert this to km/hr. Note that \(8.33 \approx 8\frac{1}{3} = \frac{25}{3}\). \[ \text{Speed}_2 = \frac{25}{3} \text{ m/s} = \frac{25}{3} \times \frac{18}{5} \text{ km/hr} = 5 \times 6 = 30 \text{ km/hr} \] Time deviations: 60 minutes = 1 hour. 300 minutes = 5 hours. 
Scenario 1: Speed \(S_1 = 50\) km/hr. Time taken \(T_1 = T - 1\) hours (since it's 1 hour earlier). Distance \(D = S_1 \times T_1 = 50(T - 1)\). (Equation 1) 
Scenario 2: Speed \(S_2 = 30\) km/hr. Time taken \(T_2 = T + 5\) hours (since it's 5 hours late). Distance \(D = S_2 \times T_2 = 30(T + 5)\). (Equation 2) Since the distance \(D\) is the same in both cases, we can equate the two expressions for \(D\). \[ 50(T - 1) = 30(T + 5) \] \[ 50T - 50 = 30T + 150 \] \[ 50T - 30T = 150 + 50 \] \[ 20T = 200 \] \[ T = \frac{200}{20} = 10 \text{ hours} \]
Step 4: Final Answer: 
The correct (scheduled) time for the train to complete its journey is 10 hours.