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the speed of an aeroplane is reduced by 40 km per hour it takes 20 minutes more to cover 1200 find the speed of the aeroplane |
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Answer» Let the actual speed of the aeroplane be 'x' km/hr So, speed after reduction = (x - 40) km/hr Let the actual time taken by the aeroplane be y hr and the time taken after the speed reduction = y + 20 min = (y + 20/60) Total distance = 1200 km So, Distance = speed*time 1200 = x*y XY = 1200 y = 1200/x .............(1) After speed reduction, 1200 = (x - 40) (y + 1/3) 1200 = (x - 40) (3y + 1/3) 1200*3 = (x -40) (3y + 1) Now, substituting the value of y = 1200/x, we get 3600 = (x - 40) (3*1200/x + 1) 3600 = (x - 40) (3600/x + 1) 3600x = (x - 40) (3600 + x) 3600x = x² + 3600x - 40x - 144000 x² - 40x - 144000 = 0 x² - 400x +360x - 144000 = 0 x(x - 400) + 360 (x - 400) = 0 (x - 400) (x + 360) x = 400 and x = -360 Speed can't be NEGATIVE, so the actual speed of the aeroplane is 400 km/hr substituting the value of y = 1200/x. y = 1200/400 y = 3 hours So, the actual time taken by the aeroplane is 3 hours. |
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