Question

A plane left 30 minutes later than the scheduled time and in order to reach the desination, 1500km away in time. It has to increase the speed by 250 km/h from the usual seed. Find the usual speed? What value is reflected in this question.

Answer 1

Answer:

Explanation:

Solution :-

Let the usual speed of the plane be x km/h.

Time taken to cover 1500 km with usual speed = 1500/x hours

Time taken to cover 1500 km with the speed of (x + 250) km/h = 1500/x + 250 hours

According to the Question,

⇒ 1500/x - 1500/x + 250 = 1/2

⇒ 1500(x + 250) - 1500x/x² + 250x = 1/2

⇒ 1500x + 1500 × 250 - 1500x/x² + 250x = 1/2

⇒ 1500 × 250 = x² + 250x

⇒ 750000 = x² + 250 = 0

⇒ x² + 250x - 750000 = 0

⇒ x² + 1000x - 750x - 750000 = 0

⇒ x(x + 1000) - 750(x + 1000) = 0

⇒ (x - 750) (x + 1000) = 0

⇒ x = 750, - 1000 (Neglecting negative sign)

⇒ x = 750 km/h

Hence, the usual speed is 750 km/h

Answer 2

QUESTION :

A plane left 30 minutes later than the scheduled time and in order to reach the desination, 1500km away in time.

It has to increase the speed by 250 km/h from the usual speed.

Find the usual speed?

What value is reflected in this question.

SOLUTION :

Let the original speed of the plane be X km ph.

New speed of the plane = { X + 250 } km ph.

T 1 =[ 1500 / X ] hr.

T 2 = [ 1500 / X + 250 ] hr

T2 - T1 = 30 mins = ( 1 / 2 ) hr

=> [ 1500 / X ] - [ 1500 / X + 250 ] = ( 1 / 2 )

=> X ^ 2 + 250 X - 7500 = 0

=> X^2 + 1000 X - 750 X - 7500 = 0

=> X ( X + 1000 ) - 750 ( X + 1000 ) = 0

=> ( X - 750 ) ( X + 1000 ) = 0

=> X = 750 kmph.

So the usual speed of the plane is 750 kmph.