Question

Places A and B are 200 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
[Substitution Method] [ 2 marks ]

Answer 1

Solution:

​​​​​​​Let the speed of the cars be $xkm/hr$ and $ykm/hr$.

Distance between 2 cars is 200 km.

When the cars travel in the same direction,

Distnace traveled by 1st car in 4 hrs is $4xkm$ [distance = speed $\times$ time]

Distnace traveled by 2nd car in 4 hrs is $4ykm$

$\therefore 4x-4y=200$

$\Rightarrow x-y=50\dots \dots \left(i\right)$

When the cars travel in the same direction,

Distnace traveled by 1st car in 1 hr is $xkm$ [distance = speed $\times$ time]

Distance traveled by 2nd car in 1 hr is $ykm$

$\therefore x+y=200\dots \dots \left(ii\right)$ (1 mark)

Solving equation (i) and (ii),

$x=50+y$ [From (i)]

Substituting value of x in (ii)

$x+y=200$

$50+y+y=200$

$50+2y=200\Rightarrow y=75$

Now, $x=50+y$

$x=50+75\Rightarrow x=125$

$\therefore x=125,y=75$ (1 mark)