Question

Two persons ride towards each other from two places 55 km apart, one riding at 12 km/h and the other at 10 km/h. When will they be 11 km apart?

• A. 2 h and 30 min
• B. 1 h and 30 min
• C. 2 h
• D. 2 h and 45 min

Hint:

For objects moving towards each other, relative speed is the sum of speeds. Remember to consider both before and after meeting.

Answer 1

The Correct Option is C

To solve the problem of determining when two people riding towards each other from a distance of 55 km will be 11 km apart, we can follow these steps:

1. Understand the Problem: Two cyclists start riding towards each other from a 55 km distance apart. One cyclist rides at 12 km/h, and the other at 10 km/h. We need to find the time when they will be 11 km apart.
2. Analyze Given and Required Information:
   • Initial Distance between two cyclists = 55 km
   • Relative Distance we need to find = 11 km (so they should have covered 55 km - 11 km = 44 km jointly)
   • Speed of the first cyclist = 12 km/h
   • Speed of the second cyclist = 10 km/h
   • Total Relative Speed = 12 km/h + 10 km/h = 22 km/h
3. Calculate Time Taken to Cover Joint Distance:
   • Distance covered when they are 11 km apart = 44 km
   • Time taken = \(\frac{44 \text{ km}}{22 \text{ km/h}}\)
   • Time taken = \(2\) hours
4. Conclusion: The two riders will be 11 km apart after 2 hours, making the correct answer: 2 h.
5. Review Other Options:
   • 2 h and 30 min: This would mean covering 55 - 11 km = 44 km at a speed greater than \(22 \text{ km/h}\), which isn't possible with the given speeds.
   • 1 h and 30 min: This would mean covering 44 km at a speed of \(\frac{44}{1.5}\approx 29.33 \text{ km/h}\), which is not feasible as their combined speed is 22 km/h.
   • 2 h and 45 min: This would indicate a much slower cumulative speed than possible with their given speeds of 22 km/h.

Thus, based on calculations and logical elimination, the solution is correct with the answer being 2 hours.