Question

an aeroplane left 50 minutes later than its scheduled time and in order to reach its destination 1250 kilometre away it had to increase its speed by 250 km per hour from its original speed​

Answer 1

Answer:

Actual time taken is 2.5 hrs or 2 hrs and 30 mins.

Step-by-step explanation:

I believe your Question was,

"An Aeroplane left 50 minutes later than its scheduled time and in order to reach the destination 1250 km away in time had to increase its speed by 250km/h from its actual time. Find its usual time taken to arrive"

Case 1 (If it wasn't late)

Let the actual speed of the Aeroplane be 'x' km/h

We know that the distance travelled = 1250 km

Then, its usual arrival time must be 1250/x

Let the time be T1 = (1250/x) hrs

(Because speed = distance/time,

so, time = distance/speed)

Case 2 (When it became late)

Now the plane here was late, so its speed was increased by 250km/h

then, its speed now will be (x + 250) km/h

Thus, time taken will be ((1250)/(x + 250)) hrs

Let the time be T2 = ((1250)/(x + 250)) hrs

Now, we know that the plane was 50 minutes late

then, T1 - T2 = 50/60

because T1 and T2 are in hours

(BUT REMEMBER IT CAN'T BE T2 - T1 = 50, IF YOU HAVE DIFFICULTY IN FINDING WHICH MUST BE SUBTRACTED, I WILL SHARE WITH YOU AN EASY METHOD

SPEED = DISTANCE/TIME

HERE WE USED, TIME = DISTANCE/SPEED

WE SHOULD REMEMBER THAT IF SPEED INCREASES, TIME DECREASES AND IF SPEED DECREASES TIME INCREASES, SEE HERE THE SPEED WAS INCREASE AND SO TIME BECAME T2. SO, T2 WILL BE SMALLER THAN T1. THUS WE GET T1 - T2 = 50/60)

But we said T1 = 1250/x and T2 = (1250)/(x + 250)

so,

T1 - T2 = 50/60

= (1250/x) - (1250)/(x + 250) = 50/60

= 1250((1/x) - (1/(x + 250)) = 50/60

= 1250((x + 250) - x)/(x)(x + 250)) = 50/60

= 1250((250/(x² + 250x)) = 50/60

= 1250 × 250 = (50/60) × (x² + 250x)

= 1250 × 250 × 60 = 50(x² + 250x)

= (1250 × 250 × 60)/50 = x² + 250x

= x² + 250x = 375000

= x² + 250x - 375000 = 0

ax² + bx + c = 0

where a = 1, b = 250, c = -375000

By splitting the middle term method we get,

Sum = b = 250

Product = a × c = - 375000

Thus, factors are 750 and - 500

x² + 750x - 500x - 375000 = 0

x(x + 750) -500(x + 750) = 0

(x - 500)(x + 750) = 0

so, x = 500 or x = -750

we know that x is speed and speed can't be negative

so, x = 500

Now, T1 is the actual time

T1 = 1250/x = 1250/500 = 2.5 hrs or 2 hrs and 30 mins.

If you didn't understand this typing I have put up an image for you do check that

Hope it helped and you understood it........All the best