SOLUTION: a boy rides a bicycle at a certain rate for 5 km then decreases his rate by 2 km per hour and rode another 6 km. Find his original rate if he rode for a total of 140 minutes

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a boy rides a bicycle at a certain rate for 5 km then decreases his rate by 2 km per hour and rode another 6 km. Find his original rate if he rode for a total of 140 minutes      Log On


   

Question 999016: a boy rides a bicycle at a certain rate for 5 km then decreases his rate by 2 km per hour and rode another 6 km. Find his original rate if he rode for a total of 140 minutes
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
              rates        time       distance
part 1         r            5/r       5
part 2         r-2          6/(r-2)   6
total                       7/3

Time sum equation, highlight_green%285%2Fr%2B6%2F%28r-2%29=7%2F3%29
Simplest denominator 3r%28r-2%29;

3r%28r-2%29%285%2Fr%2B6%2F%28r-2%29%29=3r%28r-2%29%287%2F3%29
3%2A5%28r-2%29%2B3%2A6%2Ar=r%28r-2%29%2A7
15r-30%2B18r=7r%5E2-14r
33r-30=7r%5E2-14r
0=7r%5E2-14r-33r%2B30
highlight%287r%5E2-47r%2B30=0%29
Try formula for general solution to find r.
Discriminant is 47%5E2-4%2A7%2A30=2209-28%2A30=1369
which is 37%5E2
-
r=%2847%2B-+37%29%2F%282%2A7%29
r=%2847%2B-+37%29%2F14, seems strange that both would be positive;
Either r=10%2F14=5%2F7 Or r=84%2F14=%287%2A12%29%2F%287%2A2%29=6
Reasonable result may best be highlight%28highlight%28r=6%29%29.
The subtraction of the "2" for the part_2 rate would make this to be the reasonable value for rate of part 1.