Question

An aeroplane takes 1 hour less for a journey of 1200km, if its speed is increased by 100km/ hrfrom its usual speed. Find the usual speed.

Answer 1

Let the Usual Speed of the aircraft be S, and time taken be t. Distance = 1200km 

Time = Distance/ Speed. 

Time taken is reduced by 1 hr when speed increases by 100 km/ hr

`1200/"S" = 1200/("S" + 100) + 1`

`=> (1200 + "S" + 100)/("S" + 100) = 1200/"S"`

⇒ 1300S + S² = 1200 S + 120000 

⇒  S² + 100 S - 120000 = 0

⇒  S² + 400 S - 300 S - 120000 = 0 

⇒  S (S + 400) - 300 (S + 400) = 0 

⇒  (S + 400) (S - 300) = 0 

⇒  S= -400 ,300

Speed cannot be negative .

Hence, S=300 km/ kr