SOLUTION: A car travels 200km on a main highway and then travels 30km/h slower on a secondary highway for 160km. The trip took 6 hours in total. Set up a rational equation that models this

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A car travels 200km on a main highway and then travels 30km/h slower on a secondary highway for 160km. The trip took 6 hours in total. Set up a rational equation that models this      Log On


   

Question 1136702: A car travels 200km on a main highway and then travels 30km/h slower on a secondary highway for 160km. The trip took 6 hours in total.
Set up a rational equation that models this situation and use it to algebraically determine the speed on the main highway.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
highlight_green%28200%2Fr%2B160%2F%28r-30%29=6%29

r, car speed on main highway

-
r, speed
x, time
d, distance
-
system%28rx=d%2Cx=d%2Fr%29 

                       SPEEDS        TIMES        DISTANCES

Main hwy               r            200/r          200

Secondary hwy          r-30         160/(r-30)     160

TOTAL                                6

Sum of the time quantities totals 6 hours.

200%2Fr%2B160%2F%28r-30%29=6
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100%2Fr%2B80%2F%28r-30%29=3
100%28r-30%29%2B80r=3r%5E2-90r
270r-3000=3r%5E2
90r-1000=r%5E2
r%5E2-90r%2B1000=0
.
.
highlight%28r=77%29