SOLUTION: Nickola swam at a rate of 2 ​km/hr and ran at a rate of 11 ​km/hr for a total distance traveled of  68.5 km. If he completed the race in 9.5 ​hours, how long did he take

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Question 1137307: Nickola swam at a rate of 2 ​km/hr and ran at a rate of 11 ​km/hr for a total distance traveled of  68.5 km. If he completed the race in 9.5 ​hours, how long did he take to complete each part of the​ race?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
         speed          time          distance

swam        2           9.5-x       2(9.5-x)

ran        11            x           11x

total                    9.5           68.5

2%289.5-x%29%2B11x=68.5
-
19-2x%2B11x=68.5
9x%2B19=68.5
9x=68.5-19
x=5.5
.
.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Nickola swam at a rate of 2 ​km/hr --- let time be x hours
and ran at a rate of 11 ​km/hr -------- let time be y hours
total distance traveled of  68.5 km. Distance = speed x time
So 2x+11y =68.5 .........(1)
he completed the race in 9.5 ​hours,
Time swimming + time running = 9.5 hours
x+y=9 ................ (2)
time swimming x hours
time running y hours

x + y = 9.5 .............1
2 x + 11 y = 68.5 .............2
Eliminate y
multiply (1)by -11
Multiply (2) by 1
-11 x -11 y = -104.5
2 x 11 y = 68.5
Add the two equations
-9 x = -36
/ -9
x = 4
plug value of x in (1)
x + y = 9.5
4 + y = 9.5
y = 9.5 -4
y = 5.5

time swimming 4 hours
time running 5 1/2 hours