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Starting from his house one day, a student walks at a speed of $$2\frac{1\ }{2}$$ kmph and reaches his school 6 minutes late. Next day he increases his speed by 1 kmph and reaches his school 6 minutes early. How far is the school from the house?
Assume the distance to be $$x$$ km.
When he travels at the speed of 2.5 km/hr he is 6 minutes late.
When he travels at the speed of 3.5 km/hr he is 6 minutes early
$$\frac{\ x}{2.5}$$ - $$\frac{\ x}{3.5}$$ = $$\frac{\ 12}{60}$$
$$\frac{\ 2x}{5}-\frac{\ 2x}{7}\ =\frac{\ 1}{5}$$
$$\frac{\ 4x}{35}=\frac{\ 1}{5}$$
$$\ x=\frac{\ 7}{4}=\ 1\frac{\ 3}{4}$$ km
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