Question

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

Answer 1

SOLUTION :  

Given: Total distance of a journey = 1200 km

Let the usual speed of an aeroplane be x km/h  and the increased  speed of an aeroplane is (x + 100) km/h

Time taken by an aeroplane with usual speed to cover 1200 km= 1200/x hrs

[ Time = Distance/speed]

Time taken by an aeroplane with increased speed 1200 km= 1200/(x + 100) hrs  

A.T.Q

1200/ x - 1200/(x + 100) =   1

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

[By taking LCM]

1200x + 120000 - 1200x /(x² + 100x) = 1

120000 / x² + 100x = 1

x²+ 100x  =  120000

[By cross multiplication ]

x² + 100x  -  120000  = 0

x² - 300x + 400x - 120000 = 0

[By middle term splitting]

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

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

x = 300 or  x = - 400  

Since, speed can't be negative, so x  ≠  - 400

Therefore,  x = 300 km/h  

Hence the usual speed of an aeroplane 300 km/h .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

hello mate :-)

Let the original speed of the aeroplane be = x

Time = Distance/Speed

Original time taken = 1200/x

If speed = x+100

then,

New time = 1200/x+100

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

= 1200 (x + 100) - 1200x

 = 0 x (x + 100)

= 1200x + 120000 - 1200x

 = 0 x^2 + 100x

120000 = x^2 + 100x

x^2 + 100x - 120000 = 0

x^2 + 400x - 300x - 120000 = 0

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

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

x-300 = 0

So, x = 300

or

x+400 = 0

So, x = -400

speed cannot be negative. so we will take the positive one.

So, x = Original speed = 300 km/h.