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Question
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600kms away in time, it had to incease its speed by 400km/ hr from its usual speed. Find the usual speed of the plane.
Solution
Let the Usual Speed of the aircraft be S, and time taken be t.
Distance = 1600km
Time = Distance/ Speed.
Time remains the same in both the cases. When he is late by 40 mts, his speed is increased by 400km/ hr
`1600 / "S" = 1600/("S" + 400) + 40/60`
⇒ `(96000 + 40"S" + 16000)/(60 "S" + 24000) = 1600/"S"`
⇒ 96000S + 40S2 + 16000S = 96000S + 38400000
⇒ 40S2 + 16000 S - 38400000 = 0
⇒ S2 + 400 S- 960000 = 0
⇒ S2+ 1200 S - 800S - 960000 = O
⇒ S (S +1200} - 800 (S +1200) = 0
⇒ (S +1200) (S - 800) = 0
⇒ S= 1200 ,-800 (Speed cannot be negative)
S = 800 km / hr
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