Question

The Martin family took 6 hr to paddle to a campsite 24 mi downstream. The next day, they paddled 6 hr, but were only halfway back. How fast is the stream and how fast can the Martins paddle in still water?

Answer 1

The speed of the stream is 2 mph, and the speed of the Martins in still water is 6 mph.

Step-by-step explanation:

To solve this problem, we can use the formula:

D = R * T

where D is the distance, R is the rate, and T is the time.

1. Let's assume the speed of the stream is S mph and the speed of the Martins in still water is M mph.
2. On the first day, the Martins paddle downstream, so their effective speed is (M + S) mph. They travel a distance of 24 miles in 6 hours, so we can set up the equation: 24 = (M + S) * 6.
3. On the second day, the Martins paddle upstream, so their effective speed is (M - S) mph. They travel half the distance back, which is 12 miles, in 6 hours. We can set up the equation: 12 = (M - S) * 6.
4. Now, we have a system of two equations with two variables. We can solve this system by substitution or elimination to find the values of S and M.

By solving the system of equations, we find that the speed of the stream is 2 mph and the speed of the Martins in still water is 6 mph.