Solution

Given that Bus A goes from one city to another, taking 4 hours more than Bus B. The two cities are 120 km apart. When Bus A doubles its speed, it takes 1 hour less than Bus B.

 

Let the speed of Bus A be x km/hr and the speed of Bus B be y km/hr.

According to the problem:

\({120 \over x} = {120 \over y} + 4\)

 

When Bus A doubles its speed, the new time taken by Bus A is:

\({60 \over x} = {120 \over y} - 1\)

 

Simplifying the two equations:

From the first equation:

\({120 \over x} - {120 \over y} = 4\)

 

From the second equation:

\( {120 \over y} - {60 \over x} = 1\)

 

By solving these two equations, we find:

x = 12 km/hr, y = 20 km/hr

 

Hence, the earlier speeds of Bus A and Bus B are 12 km/hr and 20 km/hr, respectively.