Question

A Plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time ,it has to increase the speed by 250 km /hr from the usual speed .Find the usual speed .​

Answer 1

C o n c e p t :

We use the formula for determining Time in terms of Distance and Speed which is, T = D / S , where T is the time, D is the distance and S is the speed of the plane.

R e q u i r e d A n s w e r :

Given Distance D = 1500km and the Speed increase by S= 250km/h also that the plane left 30 minutes later than the scheduled time.

We have to determine the usual speed of the plane

Let the usual speed of the plane be x.

We have the formula to determine Time in terms of Distance and Speed which is,Given Distance D = 1500km and the Speed increase by S= 250km/h also that the plane left 30 minutes later than the scheduled time.

We have to determine the usual speed of the plane

Let the usual speed of the plane be x.

We have the formula to determine Time in terms of Distance and Speed which is, T = D / S

where T is the time, D is the distance and S is the speed of the plane.

Substituting the values of Distance D and the Speed S (as assumed x) in above equation we get,

Time T = 1500 / x ( i )

Now given that the speed is increased by 250km/hr.

Thus, we obtain a new speed adding with the previous one x, which gives the new speed as S = x + 250

Similarly, the new time T’ becomes T = 1500 / x + 250 ( ii )

Now because we are doing all calculations in km/hour so we convert 30 mins into hour.

We have, I hour= 60 mins

60 mins= 1 hour

1 min = 1 / 6 hours

Implies 30 mins = 30 / 60 = 1 / 2 hours

That means the plane left 1 / 2 hours later than the scheduled time, thus adding the Time T to 1 / 2

hour gives us the new Time T’

Thus, T + 1 / 2 = T

Now substituting the values of T and T’ obtained by the equation (i) and (ii) we get

T + 1 / 2 = π

: $\implies$ 1500 / x + 1 / 2 = 1500 / x + 250

: $\implies$ 1500 / x - 1500 / x + 250 = 1 / 2

: $\implies$ 1500 ( x + 250 ) - 1500 x / x ( x + 250 ) = 1 / 2

: $\implies$ 1500 x + 375000 - 1500 x / x ( x + 25 ) = 1 / 2

: $\implies$ 375000 / x ( x + 250 ) = 1 / 2

Cross multiplying the above equation we get,

750000 = x² + 250 x

Rearranging the equation we get,

x² + 250 x - 750000 = 0

Now we find two numbers whose sum = + 250 and multiple = - 750000, we get possible numbers as 1000 and -750

Splitting the above equation, we get,

: $\implies$ x ² + 1000 x - 750 x - 750000

: $\implies$ x ( x + 1000 ) - 750 ( x - 750 ) = 0

: $\implies$ ( x + 1000 ) ( x - 750 ) = 0

: $\implies$ x + 1000 = 0 or ( x - 750 ) = 0

: $\implies$ x = - 1000 or x = 750

Speed can't be in negative so x = 750 km / hours

• So, the usual speed of the plane is x = 750 km/hour

T i p s :

The possibility of error is that you can forget to convert 30 min in terms of hour before doing the calculation, which is wrong. We need to convert all the terms in one unit and then proceed accordingly.