A man drives his car on the highway where the speed limit is $60$ kmph. He has to cover a distance of $240$ km at a uniform speed on the road. If he increases his speed by $20$ kmph, he can reach the destination 1 hour earlier. What is his original speed?

Let the original speed be v kmph, so the original time taken is 240 divided by v hours. If the speed increases by 20 kmph, the new time becomes 240 divided by v plus 20 hours, which is 1 hour less than the original time. Setting up the equation, 240 divided by v minus 240 divided by v plus 20 equals 1, and solving yields the quadratic equation v squared plus 20v minus 4800 equals 0. Factoring this equation gives v equals 60 or v equals negative 80, and since speed must be positive, the original speed is 60 kmph.

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