Question

40 minutes late due to bad weather and in order to reach its destination thousand 600 km away in time it had to increase its speed by 400 km per hour from its usual speed then the usual speed of the plane is

Answer 1

$\textbf{Answer}$

Total distance = 1600 km

Lets suppose Original speed = x km/hr

=> $\textbf{Since, Time = Distance/Speed}$

=> $\textbf{Original time = 1600/x hr}$

Since plane gets late due to bad weather,
In that case,
$\textbf{Distance remains same}$
$\textbf{Speed is increased by 400}$
$\textbf{Time needed to travel is 40 minutes less}$

40minutes = 40/60 hours = 2/3 hours

$\textbf{New speed = x + 400}$
$\textbf{New time = 1600/(x+400)}$

But according to the question,
(1600/x) = 1600/(x+400) + 2/3

=> (1600/x) - 1600/(x+400) = 2/3

=> 1600{(1/x) - 1/(x+400)} = 2/3

=> 800{(x + 400 - x)/(x)(x+400)} = 1/3

=> 320000 × 3 = x^2 + 400x

=> x^2 + 400x - 960000 = 0

=> x^2 + 1200x - 800x - 960000 = 0

=> x(x + 1200) - 800(x + 1200) = 0

=> (x - 800) (x + 1200) = 0

=> x = 800 or x = -1200

Since x is the original speed of the plane which cannot be negative.

$\textbf{So the usual speed of plane is 800 km/hour}$

$\textbf{Hope My Answer Helped}$

$\textbf{Thanks}$

Answer 2

Answer:

Step-by-step explanation:

Distance = 1600 km

Let the usual speed be = x km/h

now we know that 

speed = distance /time

time = distance / speed

Usual time = 1600/x

Now due to bad weather the speed is increased b 400 km/ hr

which means new speed = 1600/x+400

Now it's given that the plain left 40 minutes late

which means new time = 1600/x+400 + 2/3 ( 40/60 = 2/3 hours)

1600/x = 1600/x+400 +2/3

1600/x-1600/x+400 = 2/3

1600(x+400)-1600x)/x(x+400) = 2/3

1600x + 640000-1600x/x²+400x = 2/3

640000 = 2/3(x²+400x)

640000 * 3/2 = x²+400x

960000 = x² +400x

0 = x²+400x-960000

0 = x² +1200x-800x-960000

0 = x( x+ 1200) - 800(x+1200)

0= (x+1200)(x-800)

x= -1200 or x= 800

Speed cannot be negative 

∴ usual speed = 800 km/h

:)