Question

In a flight of 6000 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 400 km/hour and time increased by 30 minutes.Find the original duration of flight.

Answer 1

Let Time = Distance / speed. Let time be 't '  and speed be 's ', then,  t = 6000/s   Distance = speed * time  , 6000 = (s - 400)(t+1/2)  (30 min. = 1/2 hour)=>  6000 = (s-400)(6000/s +1/2)  (t = 6000/s)=>       12000s = (s-400)2s(6000/s + 1/2)  (multiplying both sides 2s)=>    12000s=(s-400)(12000 + s) =>  12000s = 12000s + s2 -4800000 - 400s=>    0  = s2 -400s - 4800000=>  0 =s2   - 2400s + 2000s - 4800000=>  0 =  s (s- 2400 ) + 2000(s - 2400)=>  0 =  (s + 2000)(s-2400)=>  s= -2000, 2400Since, speed cannot be negative, we take it 2400km/hWE have already know  t = 6000/s  ;  t = 6000/ 2400 = 5/2 = 2 + 1/2 ; t = 2 hours and 30 minutes