The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

Question: The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

Solution:
Let the normal speed be x km/h
Then
80/x - 80/(x + 4) = 1
⇒ x² + 4x - 320 = 0
⇒ x(x + 20) - 16(x + 20) = 0
⇒ (x + 20 ) (x - 16) =0
∴ x = - 20, 16 [- 20 is not acceptable]
∴ x = 16 km/h

Therefore (x + 4) = 20 km/h
Therefore increased speed = 20 km/h