SOLUTION: Sam takes part in a multisport event. She can cycle at 4 times the spped that she can run, and she can paddle her kayak at half the speed she can run. The course is divided so the

Question 965115: Sam takes part in a multisport event. She can cycle at 4 times the spped that she can run, and she can paddle her kayak at half the speed she can run. The course is divided so the cycle section is 2x as long as the run and the kayak section is half as long as the run. She completes the 77k course in 5 hours. How fast does she run in kilometres per hour>
I got as far as working out the length of the course sections,
Cycle course=44k, Run=22k, Kayak=11k Total 77k. Stuck at this point.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let x be the speed that Sam can run, then she cycles at 4x and kayaks at x/2.
Let d be the run distance, then cycle distance is 2d and kayak distance is d/2
Use the formula rate * time = distance and time = distance / rate
****************************************
we then have two equations
d/x + 2d/4x + ( (d/2) / (x/2) ) = 5, note that (d/2)/(x/2) = d/2 * 2/x = d/x
d + 2d + d/2 = 77000
***********************************
solve second equation for d
multiply both sides of = by 2
2d +4d +d = 154000
7d = 154000
d = 22000
***********************
now substitute for d in first equation
22000/x + 44000/4x + 22000/x = 5
multiply both sides of = by 4x
88000 + 44000 + 88000 = 20x
20x = 220000
x = 11000
Sam's run rate is 11k/hour
check answer
22000/11000 + 44000/44000 + 22000/11000 = 5
2 +1 +2 = 5
5 = 5
answer checks

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