Question

out of 1900km vishal travelled some distance by bus and some by aeroplan bus travels average speed 60km/hr and the average speed of aeroplan is700km/hr it takes 5 hours to complete the journey find the distance vishal travelled by bus ?

Answer 1

Let time travelled on bus be 'x'hr and aeroplane be 'y' hr.
Now total time = 5hr
x + y = 5
y = 5-x
Also, total distance = 1900km
1900 = 60x + 700y

1900 = 60x +700(5-x)

1900 = 60x + 3500 - 700x

640x = 1600

x = 1600/640 = 5/2 hr

So distance travelled by bus = 60x
= 60*5/2 = 150km

Answer 2

Given:

Late = 30 min

Distance = 1500 km

Speed increase = 100 km / hr

To find:

The usual speed.

Solution:

By formula,

Speed = Distance / Time  

Since the time is unknown,  

Consider x for time,

Speed original = 1500 / x  

Time taken = ( x - 1 / 2 )  

Therefore,

Substituting the value of x,

Speed new = 1500 / (x - 1/2)  

Speed New - Speed original = 100

( 1500 / ( x - 1 / 2 ) ) - ( 1500 / x ) = 100

150 ( ( 10 / x - 1 / 2 ) - 10 / x = 100  

30 x -30 x +15 = 2x^2 - x

15 = 2x^2 - x

2x^2 - x -15 = 0

Solving,

x = -5/2

x = 3

As time cannot be negative,

The usual time taken by the plane is 3 hr

Speed original = ( 1500 / 3 ) = 500 km / hr

Hence, the usual speed of the plane is 500 km / hr

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