Question

Q. A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500
km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual
speed. (CBSE 2018-3M)
als at a certain average speed for a distance of 63 km and then travels at a distance
+​

Answer 1

Step-by-step explanation:

Let the usual speed be x km/hr.

Then, the speed taken =(x+100) km/hr

Distance =1500 km

Usual time =

usual speed

distance

=

x

1500

hrs

Time taken =

x+100

1500

hrs

It is given that Time taken=Usual time−0.5 hrs

⇒

x

1500

−

x+100

1500

=

2

1

⇒

x(x+100)

1500(x+100)−1500x

=

2

1

⇒x

2

+100x=1500×100×2

⇒x

2

+100x−300000=0

⇒x=

2

−100±

100

2

+4×300000

=

2

−100±1100

=500 or−600

Since speed cannot be negative, x=500 km/hr

∴ The usual speed of the plane is 500 km/hr.