Question

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

Answer 1

Given ;-

⇒ Time taken by the plane after the  scheduled time = 30 min

⇒ Total distance                                                     = 1500 km

⇒Increased. speed of aeroplane from the usual speed   =  250 km  / hr

To find :-

⇒Usual speed of aeroplane = ?

Sol ;-

⇒We dont know the usual speed so let us take usual speed as x.
                  
                                                Usual speed  =    x


⇒Total distance travelled by aeroplane          = 1500 km


Speed of aeroplane -


⇒Speed = Distance / Time = (1500 / x) Hrs { As we dont know time taken so                                                                      let us take it as x }
         
                                                               ⇒ {case  - 1 }

⇒Total .Time taken by the aeroplane to travel  =   ( x  -  1/2  )  Hrs

 ⇒    Distance travelled by aeroplane              =   1500 km

Therefore we get the speed as ,

⇒Speed = Distance / Time

= 1500 / (x - 1/2) Hrs                                         [ Case -  2 ]



Total. increased speed by the aeroplane is 250 km / hr .



⇒ Case - 1              -               Case - 2               =            Increased speed

⇒ [  1500   /   (  x  -  1 /2 ]  -   [ 1500  /  x ]           = 250


⇒ 1  / ( 2 x²  -   x )                                              = 1/6


⇒ 2x²    -     x                                                     = 6


⇒  (  x  -   2  )  (  2 x   + 3  )                                = 0

Therefore we get  x as 

⇒ x = 2 

⇒ So, the usual time taken by aeroplane =  2 hrs

Usual speed    =   Total distance  / Usual time taken
         
  
                      =      1500            /           2

⇒ 7 5 0 km / hr is the answer.

Answer 2

Solution :-

Let the original speed of train be x km/hr
New speed = (x + 250) 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 + 250) = 1/2
=> (1500x + 37500 - 1500x)/x(x + 250) = 1/2
=> 2(37500) = x(x + 250)
=> 75000 = x² + 250x
=> x² + 250x - 75000 = 0
=> x² + 1000x - 750x - 75000 = 0
=> x(x + 1000) - 750(x + 1000) = 0
=> (x - 750) (x + 1000) = 0
=> x = 750 or x = - 1000

∴ x ≠ - 1000 (Because speed can't be negative)


Hence,
Its usual speed = 750 km/hr