Question

Question:-

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it had to incrus its speed by 100 km 1 h from the usual speed find the usual speed?

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please give correct answers​

Answer 1

Question :-

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it had to increase its speed by 100 km per hour from the usual speed, find the usual speed?

$\large\underline{\sf{Solution-}}$

Let assume that the usual speed of the plane be x km per hour.

Case :- 1

Distance covered = 1500 km

Speed of plane = x km per hour.

So, time taken to cover 1500 km with the speed of x km per hour is

$\rm :\longmapsto\:\boxed{\tt{ t_1 = \dfrac{1500}{x} }} - - - (1)$

Case :- 2

Distance covered = 1500 km

Speed of plane = x + 100 km per hour.

So, time taken to cover 1500 km with the speed of x + 100 km per hour is

$\rm :\longmapsto\:\boxed{\tt{ t_2 = \dfrac{1500}{x + 100} }} - - - (2)$

According to statement

$\rm :\longmapsto\:t_1 - t_2 = \dfrac{30}{60}$

$\rm :\longmapsto\:\dfrac{1500}{x} - \dfrac{1500}{x + 100} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{1500(x + 100) - 1500x}{x(x + 100)} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{1500x + 150000 - 1500x}{x(x + 100)} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{150000}{x(x + 100)} = \dfrac{1}{2}$

$\rm :\longmapsto\: {x}^{2} + 100x = 300000$

$\rm :\longmapsto\: {x}^{2} + 100x - 300000 = 0$

$\rm :\longmapsto\: {x}^{2} + 600x - 500x - 300000 = 0$

$\rm :\longmapsto\:x(x + 600) - 500(x + 600) = 0$

$\rm :\longmapsto\:(x + 600)(x - 500)= 0$

$\bf\implies \:x = 500 \: \: or \: \: x = - 600 \: \{rejected \}$

So,

• Usual speed of the train = 500 km per hour

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MORE TO KNOW

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac