Question

A journey between mumbai and pune (192 km apart) takes two hours less by a car than by a truck. determine the average speed of the car if the average speed of the truck is 16 km/hr less than the car.

Answer 1

Solution:-
Let the speed of the average passenger train be 'x' km/hr.
So, the time taken by the passenger trauck = 192/x.
So, the average speed of the super fast truck = (x + 16) km/hr
So, the time taken by the super fast train = 192/(x + 16).
Given : Time taken by the passenger train to travel 192 km - time taken by super fast train to cover the distance of 192 km = 2 hours.
Therefore,
192/x - 192/(x + 16) = 2 Taking L.C.M.. we get

192x + 3072 + 192x
_______________ = 2
x (x + 16)

3072/x(x + 16) = 2 After cross multiplying, we get
3072 = 2x² + 32x
2x² + 32x - 3072 = 0
Dividing it by 2, we get
x² + 16x - 1536 = 0
x² + 48x - 32x - 1536 = 0
x(x + 48) - 32(x + 48) = 0
(x + 48) (x - 32) = 0
x = - 48 or x = 32
The speed of the train cannot be negative, therefore the speed of the passenger train is 32 km/hr
And the speed of the super fast truck is 32 + 16 = 48 km/hr

Answer 2

Answer:

The average speed of car is given by 32 m/s.

Explanation:

To find the average speed of car firstly find the time taken by car and truck. Then equate by equation in which car takes less time to travel between mumbai and pune that are 192 km apart. After that find the average speed of car.

Let the average speed of car be $x$km/h. So, the speed of truck is $x-16$km/ h. Car takes 2 h less time to travel from mumbai to pune than truck.

Time = total distance/average speed

Time taken by truck = $192/(x-6)$

Time taken by car = $192/x$

It is given that time taken by car is 2 h less than truck. So, the equation is given by

$192/x = 192/(x-16) - 2$

$192(x-16) = 192x - 2x^{2} - 32x$

$192x - 3072 = 192x - 2x^{2} -32x$

$2x^{2} + 32x - 3072 = 0$

On solving equation. The quadratic equation forms as

$x^{2} + 16x - 1536 = 0$

$(x-32)(x+48) = 0$

It has two solutions one is 32 and other is -48. As speed can not be negative. So, average speed of car is 32 km/h.