Question

Two cars leave towns 800 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour more than the other's. If they meet in 5 hours, what is the rate of the faster car? Do not do any rounding.

Answer 1

total distance = 800
distance traveled by faster car = d
distance traveled by slower car = 800 - d
slower speed = v
faster speed = v + 20
t = 5

distance = speed * time

faster car:
d = (v + 20) * 5      ----->   first equation

slower car:
800 - d = v * 5       ----->   second equation

Solve the two equations as a system of equations.

d = -5v + 800
d = 5v + 100

Add the equations:
2d = 900
d = 450

Now substitute d = 450 into equation d = 5v + 100 and solve for v.

450 = 5v + 100

350 = 5v

v = 70

The slower car's speed is 70 km/h.

The faster car's speed is 70 + 20 = 90.

Answer: The rate of the faster car is 90 km/h.