If a boy goes to school from his home at a speed of 8 km/hr, he is late by 30 minutes and if he goes at a speed of 12 km/hr, he reaches on time. The distance from his home to school is ______.
12 km
12 km is correct.
Time = distance ÷ speed. The same distance covered at two speeds takes different times, and the given gap between those times forms one equation in the distance.
Let the distance be \(d\) km. The slower trip takes 30 minutes, that is \(\dfrac{1}{2}\) hour, longer than the faster one.
\(\dfrac{d}{8} - \dfrac{d}{12} = \dfrac{1}{2}\)
\(\dfrac{3d - 2d}{24} = \dfrac{d}{24} = \dfrac{1}{2}\), so \(d = 12\).
So the school is 12 km from his home.
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