A car travels 60 miles in the same time that a car traveling

A car travels 60 miles in the same time that a car traveling 10 miles per hour faster travels 90 miles. What is the rate of each car?

Solution

x = rate of the first car.
x+10 = rate of the second car.
h = time in hours.

general formula is rate * time = distance

first car:

x*h = 60

second car:

(x+10)*h = 90

solve for one of the variables in the first equation in terms of the other variable and substitute in the second equation.

x*h = 60

solve for h to get:

h = 60/x

substitute in the second equation to get:

(x+10)*h = 90 becomes:

(x+10)*(60/x) = 90

multiply both sides of the equation by x to get:

(x+10)*60 = 90*x

simplify by removing parentheses to get:

60*x + 600 = 90*x

subtract 60*x from both sides of the equation to get:

600 = 90*x - 60*x = 30*x

divide both sides of the equation by 30 to get:

x = 20

use the value of x to solve for h in the first equation.

x*h = 60 becomes:

20*h = 60

divide both sides of the equation by 20 to get:

h = 60/20 = 3

use value of x and h in the first equation to get:

x*h = 60 becomes:

20*3 = 60 which is true.

use value of x and h in the second equation to get:

(x+10)*h = 90 becomes:

(20+10)*3 = 90

combine like terms to get:

30*3 = 90 which is also true.

answer is:

first car travels at 20 miles per hour.

second car travels at 30 miles per hour.