Question

A car takes 4 hours to reach a destination traveling at a speed of 63 km/h. How long will it take to cover the same distance if the car travels at the speed of 56 km/h? Do these quantities (time and speed) vary directly or inversely? Find the constant of variation.

Answer 1

It will take 4.5 hours.

The quantities vary inversely.

The constant variation is 252.

Image:

Answer 2

It will take 4.5hrs to cover the same distance

The constant of variation,k=252

Step by step explanation

Given that,

`speed = (distance)/(time)`

From the question

Time=4hr

Speed=63km

By substitution we obtain,

`63= (distance)/(4)`

Cross multiplying we get,

`distance=63 * 4`

`distance=252km`

Now,

speed=56km

Distance Covered=252km

By substitution:

We obtain,

`56= (252)/(time)`

Cross multiply

`56* time=252`

Divide through by 56

`time= (252)/(56)`

`time=4.5hrs`

From the formula,

`speed= (distance)/(time)`

Which means that, speed and time varies inversely.

`speed\propto (1)/(time)`

Let k be variation constant

This implies that

`speed = k * (1)/(time)`

`k=speed *{time}`

Taken,

Time=4hrs

speed=56km

`k=56*4`

`k=252`