SOLUTION: A girl walks 24 km at the speed of x km/hr and 40 km at the speed of y km/hr on 1st day. she walks total for 9 hrs on that day. on the next day she walks 18 km at the speed of x km

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Question 732470: A girl walks 24 km at the speed of x km/hr and 40 km at the speed of y km/hr on 1st day. she walks total for 9 hrs on that day. on the next day she walks 18 km at the speed of x km/hr and 48 km at the speed of y km/hr. On that day also she walks for total 9 hrs.Find x and y?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Day 1:
24%2Fx%2B40%2Fy=9 hours.
Multiply both sides by xy.
24y%2B40x=9xy

Day 2:
18%2Fx%2B48%2Fy=9 hours.
Multiply both sides by xy.
18y%2B48x=9xy

Those equations might be good to use, but maybe taking the first form of those equations, and trying substitution is better or easier. The system is not linear in x and y.

Day 1 equation, 24%2Fx%2B40%2Fy=9,
40%2Fy=9-24%2Fx
40%2Fy=9x%2Fx-24%2Fx
40%2Fy=%289x-24%29%2Fx
1%2Fy=%289x-24%29%2F%2840x%29
highlight%28y=%2840x%29%2F%289x-24%29%29

Day 2 equation,
18%2Fx%2B48%2Fy=9
18%2Fx=9-48%2Fy
18%2Fx=%289y-48%29%2Fy
x%2F18=y%2F%289y-48%29
highlight%28x=%2818y%29%2F%289y-48%29%29
Substitute for y,...
x=%2818%2840x%2F%289x-24%29%29%29%2F%289%28%2840x%29%2F%289x-24%29%29-48%29
.
...so manyy steps,...
.
x=10x%2F%28-x%2B16%29
.
x%5E2-16x%2B10x=0
x%5E2-6x=0
x%28x-6%29=0
cross%28x=0%29 OR highlight%28x=6%29
You can continue onward to solve for y.