Two people paddle a canoe 8 miles upstream in two hours. They then turn around and paddle 8 miles downstream in one hour. If they are paddling at the same rate both upstream and downstream, how fast are they paddling? How fast is the current?

Step-by-step explanation:

This question can be solved by generating two equations

let V = the speed at which they are paddling and U = the speed of the stream

they paddle the canoe up stream which is 8 miles in 2 hrs

the speed = 8 miles / 2 h = 4 mi/hr

since it is upstream;

V - U = 4 mi / hr ... (1)

downstream

V + U = 8 mi / hr ... (2)

make U subject of the formula in equation 2

U = 8 mi / h - V

substitute in equation 1

V - (8 mi / hr - V) = 4 mi/hr

2 V - 8 mi/hr = 4 mi/hr

2 V = 4 + 8 = 12 mi/hr

V = 12 / 2 = 6 mi / hr

to find how fast current was moving substitute the value of V into any of the equation

V - U = 4 mi/hr

6 mi/hr - U = 4 mi / hr

- U = 4 - 6 mi/hr = - 2 mi / hr

U = 2 mi/hr