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31. An old lady while boarding a plane got hurt 3and the captain immediately called for themedical aid. Thus the plane left with the lady,30 minutes later than the scheduled time.Then in order to reach its destination 1500 kmaway in time, it has to increase its speed by250 km/hr from its usual speed. Find theusual speed of the plane. (Delhi 2010 C) |
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Answer» Given: distance=1500km Let the original speed of a plane =x km/h New speed= x+250 ( speed increase by 250 km/h) Time taken at original speed = distance/ speed= 1500/x h Time taken at new speed = distance/ speed= 1500/x+250 h ∴ 1500/x = 1500/x+250 + 30/60 (30 min= 30 /60= 1/2 hr) 1500/x = 1500/x+250 + 1/21500/x - 1500/x+250= 1/2 (1500 (x + 250) - 150 x)/ x(x+250)= 1/2 (1500x +1500× 250 - 1500x)/ x(x+250)= 1/2 1500×250 / x² +250 x = 1/2 2(1500×250) =x² +250 x 2(375000) =x² +250 x 750000 =x² +250 x x² +250 x - 750000=0 x² +1000x - 750x -750000=0 x(x+1000) - 750(x+ 1000)=0 (x+1000) (x-750) =0 (x+1000) =0 x= -1000 ( speed cannot be negative)(x-750) =0 x= 750km/h Like my answer if you find it useful! |
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