I need help with math

Question

Two cars leave towns 600 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car?

Answer 1

Distance = Velocity X Time

 

Velocity of Car 1 = v1

Velocity of Car 2 = v2

 

System of two equations:

 

v2 = v1 - 20

 

(v1)(t) + (v2)(t) = 600

(v1)(4) + (v2)(4) = 600  (since the total distance is 600 km, and the time is 4 hours)

 

Substitute (v1 - 20) in place of v2:

 

(v1)(4) + (v1 - 20)(4) = 600

(v1)(4) + (v1)(4) - (20)(4) = 600

(v1)(8) = 680

v1 = 85

 

Plug in v1 = 85 into the v2 equation (v2 = v1 - 20):

 

v2 = 65