Question
A boy travels from his home to school by bicycle. Riding at a speed of 8 km/h, he arrives 18 minutes late. However, if he rides at a speed of 2.5 m/s, he is only 8 minutes late. What is the distance between his home and school?
Solution
ATQ,
Let the distance between the home and school be x km Time taken at 8 km/h = T₁ = x/8 hours Speed = 2.5 m/s = (2.5 × 18/5) = 9 km/h Time taken at 9 km/h = T₂ = x/9 hours Difference in time = T₁ - T₂ = (x/8) - (x/9) Given, T₁ - T₂ = 18 - 8 = 10 minutes = 10/60 = 1/6 hour So, (x/8) - (x/9) = 1/6 (9x - 8x)/72 = 1/6 x/72 = 1/6 x = 72/6 = 12 Therefore, the required distance is 12 km.
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