Math Problem Statement

Second question

The distance between points X and Y is 420 km. Point X is located at a distance of 100 km from a city C, while point Y is 60 km from city C. A bus traveling from city C reaches point X at 7:00 AM. If the bus travels at a speed of 60 km/h, at what time will the bus reach point Y?

Solution

The second question is written in Sinhala, and here's a rough translation:


Question 2:
The distance between points XX and YY is 420 km. Point XX is located at a distance of 100 km from a city CC, while point YY is 60 km from city CC. A bus traveling from city CC reaches point XX at 7:00 AM. If the bus travels at a speed of 60 km/h, at what time will the bus reach point YY?


Let me solve this:

Given:

  • Distance from XX to YY = 420 km
  • Bus speed = 60 km/h
  • Time at XX = 7:00 AM

The total time it will take to travel from XX to YY: Time=DistanceSpeed=42060=7hours\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{420}{60} = 7 \, \text{hours}

So, if the bus leaves XX at 7:00 AM, after 7 hours it will reach YY, which is at: 7:00AM+7hours=2:00PM7:00 \, \text{AM} + 7 \, \text{hours} = 2:00 \, \text{PM}

Final Answer:

The bus will reach point YY at 2:00 PM.


Would you like more details or have any questions on this? Here are five related questions for further exploration:

  1. What if the bus stopped for a 30-minute break? What time would it reach YY?
  2. How would the arrival time change if the speed of the bus was 80 km/h?
  3. If the bus departed XX at 6:00 AM instead of 7:00 AM, what would be the new arrival time?
  4. What would happen if the road between XX and YY had different speed limits?
  5. How far would the bus travel if it had to make detours along the route from XX to YY?

Tip: When solving time and distance problems, always ensure that the units (km, hours, minutes) match up to avoid calculation mistakes.

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Math Problem Analysis

Mathematical Concepts

Distance and Speed
Time Calculation

Formulas

Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 6-8