Let the original average speed of the cyclist be x km/hour. Time taken by the cyclist at the reduced average speed - Time taken by the cyclist at the original average speed = 20 minutes ∴
14
x−1
−
14
x
=
20
60
⇒
14
x(x−1)
=
1
3
⇒x2−x−42=0 ⇒(x−7)(x+6)=0 ⇒x=7 (Speed of the cyclist cannot be negative) Thus, the original average speed of the cyclist is 7 km/hour.