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A boy starts from his house and walks at a speed of 5 km/hr and reaches his school 3 minutes late. Next day he starts at the same time and increases his speed by 4 km/hr and reaches 3 minutes early. What is the distance (in km) between the school and his house?

A boy starts from his house and walks at a speed of 5 km/hr and reaches his school 3 minutes late. Next day he starts at the same time and increases his speed by 4 km/hr and reaches 3 minutes early. What is the distance (in km) between the school and his house? Correct Answer 1.125

Let the distance between the school and his house be ‘x’ km

Time taken on first day = Distance/speed = x/5 hrs.

His speed on next day = 5 + 4 = 9 km/hr.

Time taken on next day = x/9 hrs.

Now,

∵ He reached 3 min. late on the first day and reached 3 min. early the next day, this means that the difference between the time taken on the 2 days = 3 + 3 = 6 min. = 6/60 = 1/10 hrs.

⇒ x/5 – x/9 = 1/10

⇒ (9x – 5x)/45 = 1/10

⇒ 4x/45 = 1/10

⇒ x = 45/4 × 1/10

⇒ x = 1.125 km

∴ Distance between the school and his house is 1.125 km

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