Question 965115
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
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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
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solve second equation for d
multiply both sides of = by 2
2d +4d +d = 154000
7d = 154000
d = 22000
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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