Question

an old lady while boarding a plane got hurt and the csptain immediatrly called for the medical aid.thus the plane left 30minuutes later than the scheduled time.then in order to reach its destination 1500km away in time, it has to increase its speed by 250km/hr from its usual speed.find the usual speed

Answer 1

Let the usual speed of the plane is x km/hr
The time taken to cover 1500 km with speed of x km/hr = 1500/x

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

1500/x = 1500/(x+250) + 30/60
> 1500x + 1500*250-1500x/x^2+250x = 1/2
When we solve the equation we get,

x = 750, -1000

As speed cannot be negative
x = 750km/hr

Answer 2

Given: distance=1500km 

Let the original speed of a plane =x km/h

New speed= x+250                            ( speed increase by 250 km/h)

Time taken at original speed = distance/ speed= 1500/x h

Time taken at new speed = distance/ speed= 1500/x+250 h

∴ 1500/x = 1500/x+250 + 30/60                    (30 min= 30 /60= 1/2 hr)

1500/x = 1500/x+250 + 1/2
 
 1500/x - 1500/x+250= 1/2

  (1500 (x + 250) - 150 x) / x(x+250)= 1/2  

(1500x +1500 × 250 - 1500 x) / x(x+250)= 1/2  

1500 × 250 / x² +250 x = 1/2

 2(1500 × 250) =  x² +250 x

2(375000) =  x² +250 x

750000 =  x² +250 x

 x² +250 x - 750000=0

x² +1000x - 750x -750000=0

x(x+1000) - 750(x+ 1000)=0

(x+1000) (x-750) =0

(x+1000) =0

x= -1000           ( speed cannot be negative)
 
(x-750) =0

x= 750 

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Hence the original speed (usual speed) = 750 km /h

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Hope this will help you.....