Uniform motion problems

Question

An executive traveled 1930 miles by car and plane. He drove to the airport at an average speed of 60 mph and the plane averaged 350 mph. The total trip took 8 hours. How long did it take to get to the airport?

Answer 1

Set up a system of equations c as the time traveled in a car and p as the time traveled in the plane.

60c + 350p = 1930 (1)

c + p = 8 (2)

Since the questions asks how much time is taken in the car, I would solve the equation 2 for p.

p = 8 - c (3)

Substitute equation 3 into equation 1.

60c + 350(8 - c) = 1930

Use distributive property

60c + 2800 - 350c = 1930

Combine like terms

2800 - 290c = 1930

Subtract 2800 from both sides

-290c = -870

Divide both sides by -270

c = 3 hours