If a person starts from home to school at a speed of 3 km/hr and returns back home at a speed of 2 km/hr in a total of 5 hours, what is the distance between home and school?
- 6 km
- 7.5 km
- 8 km
- 9 km
Explanation
Let's break this problem down step by step:
- Let the distance between home and school be x km.
- Time taken to go to school = Distance / Speed = x / 3
- Time taken to return home = Distance / Speed = x / 2
- Total time = 5 hours, so we can set up the equation: x / 3 + x / 2 = 5
- To solve for x, we can find a common denominator (6) and add the fractions: (2x + 3x) / 6 = 5
- Combine like terms: 5x / 6 = 5
- Multiply both sides by 6 to eliminate the fraction: 5x = 30
- Divide both sides by 5 to solve for x: x = 6
So, the correct answer is: 6 km
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