Question 1101908: Members of the healthy running club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned along the same course, running at 10 km/h from the second rest stop to the first,and at 6 km/h the rest of the way to the club house. If it took a total of 2.5 h to run both ways between the club house and the first rest stop, and 3 hours to run both ways between the first and second rest stops, how far, in km, did they run altogether?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Members of the healthy running club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned along the same course, running at 10 km/h from the second rest stop to the first,and at 6 km/h the rest of the way to the club house. If it took a total of 2.5 h to run both ways between the club house and the first rest stop, and 3 hours to run both ways between the first and second rest stops, how far, in km, did they run altogether?
ch->1rs->2rs
9a+5x
2rs->1rs->ch
10y+6b
x+y=3
a+b=2.5
9a+5x=10y+6b 1st to +2nd to =2nd fro+1st fro
9a=6b
a=6b/9
a=2b/3
a+b=2.5
2b/3+b=2.5
2b+3b=7.5
5b=7.5
b=7.5/5
b=1.5
a+b=2.5
a=1
5x=10y
x=2y
x+y=3
2y+y=3
3y=3
y=1
x=2
a=1
b=1.5
10y+6b
10*1+6*1.5
10+9=19 km
check
9a+5x
9+10=19
ok
We really only needed to solve for (a and x) or (b and y).
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