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Question

Two buses left town A for town B at the same time. The speed of one of the buses was 10 mph greater than the speed of the other bus. In 3.5 hours one bus reached town B, while the other bus was away from town B at a distance equal 1/6 of the distance between A and B. Find the speed of the buses and the distance between A and B.

Answer 1

Assuming the speed of bus starting from B is V , then 

the speed for bus from A =V+10

Thus V1 = Speed of A =V+10

        V2 = Speed of B =V

If x is the distance between the cities

V1 = V+10 =x/3.5

 

V2 = V = (x/6) /3.5

 

Solving these two equations x = 420  mi

 

V =(420/3.5) -10

V= (385/3.5)=110 mi/hr

 

V₁ = 110+10

       =120mi/hr

 

V ₂= 110mi/hr

Distance between the cities = 420miles 

and speeds of buses are 120mi/hr and 110mi/hr