Jack wants to measure the distance between his scout camp and another camp upstream. He can paddle his kayak at a rate of 5 mi/hr in still water, and the rate of the river is 3 mi/hr. If it takes Jack 10 hr to paddle to the camp and back, how far is the camp?
10 mi
16 mi
18 mi
80 mi
none of the above
➳ NONE OF THE ABOVE
Let’s call the distance between the two camps “d“.
We know that Jack paddles at a rate of 5 mi/hr in still water, but he’s also going against the current of the river, which is flowing at a rate of 3 mi/hr.
So his effective speed (relative to the ground) is 5 – 3 = 2 mi/hr.
On the way to the other camp, Jack is paddling with the current, so his effective speed is 5 + 3 = 8 mi/hr.
The time it takes him to get there is given as 10 hours, so we can set up the equation:
- d/8 = 10
Solving for d, we get:
- d = 80 miles
So the distance between the two camps is 80 miles.
Now, on the way back, Jack is paddling against the current, so his effective speed is 5 – 3 = 2 mi/hr.
The time it takes him to get back is also 10 hours, so we can set up the equation:
- d/2 = 10
Solving for d, we get:
- d = 20 miles
So the distance between the two camps is 20 miles.
But we know that the distance is the same both ways, so we need to average the two distances:
(d1 + d2)/2 = (80 + 20)/2 = 50
Therefore, the distance between the two camps is 50 miles.
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