Question

an aeroplane takes 1 hour less for a journey of to 1200 km if its speed is increased by 100 km per hour from his usual speed find its usual speed

Answer 1

$\colorbox{cyan}{hello}$

Let the usual speed of the aeroplane ne x km/h.

Then,

1200/x - 1200/(x + 100) = 1

=> [1200(x + 10) - 1200x] / x(x + 100) = 1

=> 1200x + 12000 - 1200x = x² + 100x

=> x² + 100x - 12000 = 0

=> x² + 400x - 300x - 12000 = 0

=> x(x + 400) - 300(x + 400) = 0

=> (x + 400)(x - 300) = 0

So,

x = - 400 or x = 300

Since, speed cannot be negative.

Therefore,

Usual speed of the aeroplane is 300 km/h.

HOPE IT HELPS

Answer 2

Let original speed be x.

time = distance/speed

original time = 1200 / x

new time = 1200 / x+100

1200 / x - 1200 / x + 100 = 1

1200 (1 / x - 1 / x + 100)=1

1200 (x + 100 - x / x* +100x) =1 here x* is x square.

120000 = x * + 100x

x * + 100x -120000 =0

therefore by solving equation

x = 300 km/hr



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