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Question

An aeroplane travelled a distance of 400km at an average speed of x km/hr . On return journey the speed was increased by 40km/hr . If it takes 30 minutes less in return journey , find the value of x .

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Solution

The expression for the onward journey:

Speed = distance/time travelled

Time taken = distance travelled/speed

1)the expression will be :

distance/speed = 400km/xkm/hr = 400/x hrs


if the return journey took 30 minute less:

then, 400/x+40 hrs + 1/2 hr = 400/x hrs
400x + x² + 40 x = 800x + 1600
x² - 360x - 1600= 0....the equation

find value of x:
x² - 360x -1600 = 0
can also be written as; x² - 400x + 40x - 1600=0
x(x-400) + 40(x-400)=0
(x+40)(x-400)=0
Therefore either x + 40 = 0 or x -400 = 0
Hence x is either = -40 or 400
Therefore x = 400km/hr



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