SOLUTION: a girl travels 10 km in 50 minutes if she runs for 8 km and walks for 2 km. if she runs for 4 km and walks 6 km, her time is 1 hour 15 minutes. find her running and walking speeds.

Question 866305: a girl travels 10 km in 50 minutes if she runs for 8 km and walks for 2 km. if she runs for 4 km and walks 6 km, her time is 1 hour 15 minutes. find her running and walking speeds.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
running speed------------x
walking speed------------y
t=d/r
8/x + 2/y = 5/6 ( hours)
4/x + 6/y = 5/4 (hours)
let 1/x = a and 1/y =b
8a+2b=5/6
4a+6y=5/4
8 a + 2 b = 5/ 6 .............1
Total value
4 a + 6 b = 5/ 4 .............2
Eliminate y
multiply (1)by -3
Multiply (2) by 1
-24 a -6 b = -5/ 2
4 a + 6 b = 5/ 4
Add the two equations
-20 a = -5/ 4
/ -20
a = 1/16
plug value of a in (1)
8 a + 2 b = 5/ 6
1/ 2 + 2 b = 5/ 6
2 b = 5/ 6 -1
2 b = 1/ 3
b = 1/ 6
a= 1/16 . Therefore x =16 km/h running speed
b= 1/ 6 Therefore y = 6 km/h walking speed
m.ananth@hotmail.ca

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