SOLUTION: A semi-truck travels 300 miles through the flatland in the same amount of time that it travels 180 miles through mountains. The rate of the truck is 20 miles per hour slower in th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A semi-truck travels 300 miles through the flatland in the same amount of time that it travels 180 miles through mountains. The rate of the truck is 20 miles per hour slower in th      Log On


   

Question 40795This question is from textbook Beginning Algebra
: A semi-truck travels 300 miles through the flatland in the same amount of time that it travels 180 miles through mountains. The rate of the truck is 20 miles per hour slower in the mountains than in the flatland. Find both the flatland rate and the mountain rate. This question is from textbook Beginning Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = the trucks rate in the mountains
r + 20 will be the rate on flat land
The semi-truck travels 300 miles through the flatland in the same amount of time that it travels 180 miles through mountains.
Let t = the time for both trips
t = 180/r
t = 300/(r + 20)
180/r = 300/(r + 20)
multiply both sides by r(r+20)
180(r+20) = 300r
180r + 3600 = 300r
subtract 180r from both sides
3600 = 120r
r = 30 the rate in the mountains
r + 20 = 50 the rate on flat land
check
180/r = 300/(r + 20)
180/30 = 300/50
6 = 6
OK