Places A and B are 80 km apart from each other on a . . .

Question : Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.

Doubt by Mehak

Solution : 

Let the speed of car at A = x km/h

and the speed of car at B = y km/h

Case I : When both the cars move in the same direction then they meet at point C after 8 hours. 

A_____B____C

We know, 

Speed = Distance/Time

Distance = Speed × Time

Distance covered by car A in 8 hours
AC = x(8) = 8x km

Distance covered by car B in 8 hours
BC = y(8) = 8y km

AB = 80 km (Given)

ATQ
AC-BC=AB
8x-8y=80
8(x-y)=80
x-y=80/8
x-y=10 — (1)

Case 2 : When both the cars move towards each other then they are meet point C after 1 hour 20 minutes i.e. 
1 hours + (20/60) hours
= 1 hours + 1/3 hours
= 4/3 hours 

A____C_____B

Distance covered by car A in 4/3 hours
AC = x(4/3) = 4x/3 km

Distance covered by car B in 4/3 hours
BC = y(4/3) = 4y/3 km

AB = 80 km (Given)

ATQ

AC+BC=AB

4x/3+4y/3=80
(4/3)(x+y)=80
x-y=[80×3]/4
x+y=60 — (2)

solving equation (1) and (2)

 x+y=60

 x- y=10
-  +    -

---------------
0 + 2y = 50

---------------

y=50/2
y=25

putting in equation (1)

x-25=10
x=10+25
x=35

Hence, the speed of car at A = 35 km/h
and speed of car at B = 25 km/h