Question

plane left 30 minutes late than the schedule time and in order to reach its destination 1500 km away in time,it has to increase its speed by 100 km/h from its usual speed.find its usual speed.

Answer 1

Answer:

Step-by-step explanation:

usual speed = 1500/x

according to question

1500/x - 30 = 1500/x +100

1500/x-1500/x+100 = 30 / 60

1500x + 150000 -1500x / x² + 100x =30 / 60

150000/ x² + 100x =30 / 60

150000 X 60 / 30 =x²+100x

300000 = x²+100x

x²+ 100x-30000

x²+ 600x-500x-30000

x(x+600) -500 (x+600)

x= 500kmph

so the usual speed is 500kmph

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Answer 2

Solution :-

Let the original speed of train be x km/hr
New speed = (x + 100) km/hr

We know that,
Time = Distance / Speed

Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.

According to the question,

=> 1500/x - 1500/(x + 100) = 1/2
=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2
=> 2(15000) = x(x + 100)
=> 30000 = x² + 100x
=> x² + 100x - 30000 = 0
=> x² + 600x - 500x - 30000 = 0
=> x(x + 600) - 500(x + 600) = 0
=> (x - 500) (x + 600) = 0
=> x = 500 or x = - 600

∴ x ≠ - 600 (Because speed can't be negative)


Hence,
Its usual speed = 500 km/hr