SOLUTION: A car drove from a city A to a city B.The distance between the two cities is 350 km.After 200km, the speed of the car decreased by 20 km/h. The total trip took 5 hours. Find the sp

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A car drove from a city A to a city B.The distance between the two cities is 350 km.After 200km, the speed of the car decreased by 20 km/h. The total trip took 5 hours. Find the sp      Log On


   

Question 1107071: A car drove from a city A to a city B.The distance between the two cities is 350 km.After 200km, the speed of the car decreased by 20 km/h. The total trip took 5 hours. Find the speed of the car in the first part of the journey.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
                    speed      time         distance
part1                r         200/r         200
part2               r-20       150/(r-20)    150
total                          5

200%2Fr%2B150%2F%28r-20%29=5
Simplify and solve this for r.
40%2Fr%2B30%2F%28r-20%29=1
40%28r-20%29%2B30r=r%5E2-20r
40r-800%2B30r=r%5E2-20r
r%5E2-20r-70r-800=0
r%5E2-90r-800=0
r=%2890%2B-+sqrt%288100%2B4%2A800%29%29%2F2
r=%2890%2B-+sqrt%284900%29%29%2F2
r=%2890%2B-+70%29%2F2
r=%2845%2B-+35%29
cross%28r=5%29 or highlight%28r=80%29
The 80 km per hour is the one which makes sense.