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Derek can paddle his kayak 6 miles per hour in still water. It takes him as long to paddle 10.5 miles upstream as it takes him to travel 31.5 miles downstream. Determine the speed of the river's current.

Respuesta :

FaDaReAdEoLa

Answer:

3 mph

Step-by-step explanation:

Let the speed of the river's current be x

Upstream (against the river's current)

Resultant velocity = 6 - x

Distance covered = (6-x)t

10.5 = (6-x)t

t = 10.5/(6-x)

Downstream (with the river's current)

Resultant velocity = 6+x

Distance covered = (6+x)t

t = 31.5/(6+x)

Therefore.......

10.5/(6-x) = 31.5/(6+x)

10.5(6+x) = 31.5(6-x)

63 + 10.5x = 189 - 31.5x

Collect like terms

42x = 126

x = 3 miles per hour

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