Question

The speed of the current in a creek is 2mph. A person can kayak 10 mi upstream in the same time that it takes him to kayak 14 mi downstream. How long will it take the person to kayak 28 mi downstream?

Answer 1

Answer:

  2 hours

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

For a kayak speed of k miles per hour in still water, the speed upstream is (k-2) and the speed downstream is (k+2). Over the distances given, the times are the same, so we can write ...

  10/(k-2) = 14/(k+2)

Multiplying by (k+2)(k-2) gives ...

  10(k+2) = 14(k -2)

  10k +20 = 14k -28 . . . . . eliminate parentheses

  48 = 4k . . . . . . . . . . . . . . add 28-10k

  12 = k

Then the time for 28 miles downstream is ...

  time = 28 / (12 +2) = 2 . . . . hours

It will take the person 2 hours to kayak 28 miles downstream.