Question

A car left 30 minutes later than scheduled time in order to reach its destination 150km away in time .it has to increase its speed by 25kmph from it usual speed find its usual speed
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Answer 1

A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from the usual speed. find its usual speed

A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from the usual speed. Find its usual speed
Sol: Let the usual time taken by the aeroplane = x km/hr Distance to the destination = 1500 km Case (i) Speed = Distance / Time = (1500 / x) Hrs   Case (iI) Time taken by the aeroplane = (x - 1/2) HrsDistance to the destination = 1500 km Speed = Distance / Time = 1500 / (x - 1/2) Hrs   Increased speed = 250 km/hr   ⇒ [1500 / (x - 1/2)] - [1500 / x] = 250 ⇒ 1/(2x2 - x) = 1/6 ⇒ 2x2 - x = 6 ⇒ (x - 2)(2x + 3) = 0 ⇒ x = 2 or -3/2 Since, the time can not be negative, The usual time taken by the aeroplane = 2 hrs and the usual speed = (1500 / 2) = 750 km/hr.

Answer 2

Answer:

Step-by-step explanation:

Let the usual speed of the car be X km/hr

Distance travelled =150km.

Time taken to travel (t¹)= 150/X

Also,

The speed increased = X +25 km/hr

So, time taken = (t²)=150/X + 25

Now,

According to the question ,we have,

t¹ - t² =30/60

150/X - 150/X + 25 = 1/2

150( X +25) - 150(X) / X(X+25)= 1/2

150X+3750 -150 X/ X² + 25X= 1/2

3750/X² + 25X= 1/2

2(3750) = 1(X² + 25X)

7500 = X² + 25X

X² + 25X - 7500=0

X² + 100X - 75 X- 7500=0

X (X + 100) -75( X +100)

(X+ 100)(X -75)

So, X = -100(speed can't be negative

.hence neglected)

or

X = 75

So , usual Speed = 75 km/hr