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

Answer:

It will take 4.5hrs to cover the same distance

The constant of variation,k=252

Step by step explanation

Given that,

$speed = \frac{distance}{time}$

From the question

Time=4hr

Speed=63km

By substitution we obtain,

$63= \frac{distance}{4}$

Cross multiplying we get,

$distance=63 \times 4$

$distance=252km$

Now,

speed=56km

Distance Covered=252km

By substitution:

We obtain,

$56= \frac{252}{time}$

Cross multiply

$56\times time=252$

Divide through by 56

$time= \frac{252}{56}$

$time=4.5hrs$

From the formula,

$speed= \frac{distance}{time}$

Which means that, speed and time varies inversely.

$speed\propto \frac{1}{time}$

Let k be variation constant

This implies that

$speed = k \times \frac{1}{time}$

$k=speed \times{time}$

Taken,

Time=4hrs

speed=56km

$k=56\times4$

$k=252$