Question

Cars A and B leave a town at the same time. Car A heads due south at a rate of 80 km/hr and car B heads due west at a rate of 60 km/hr. How fast is the distance between the cars increasing after three hours?

Answer 1

Given,

Speed of car A $\[ = 80km/hr\]$

Direction of car A = South

Speed of car B $\[ = 60km/hr\]$

Direction of car B = West

Solution,

Distance travelled by car A in 3 hours in South direction,

$\[\begin{array}{l} = 80 \times 3\\ = 240km\end{array}\]$

Distance travelled by car B in 3 hours in West direction,

$\[\begin{array}{l} = 60 \times 3\\ = 180km\end{array}\]$

Difference in distance between two cars in three hours,

$\[\begin{array}{l} = 240 - 180\\ = 60km\end{array}\]$

Distance between the cars after three hours,

$\[\begin{array}{l} = \sqrt {{{240}^2} + {{180}^2}} \\ = \sqrt {90000} \\ = 300km\end{array}\]$

Calculate the rate of distance between the cars increasing after three hours,

$\[\begin{array}{l} = \frac{{300km}}{{3hr}}\\ = 100km/hr\end{array}\]$

Hence, car A moves faster than car B at the rate of $\[100km/hr\]$ after three hours.