Question

Laura and Brent paddled a canoe 6miles upstream in 4 hrs. The return trip took 3 hr. Find the rate at which Laura and Brent paddled in still water

Answer 1

Let's say the rate at which Laura and Brent paddled in still water is "r" (in miles per hour).

When they travel upstream, they are fighting against the current, so their effective speed is (r - c) where "c" is the rate of the current (in miles per hour). They cover a distance of 6 miles in 4 hours, so we can write the equation:
6 = (r - c) * 4

When they travel downstream, they are aided by the current, so their effective speed is (r + c). This time, they cover a distance of 6 miles in 3 hours, so the equation is:
6 = (r + c) * 3

Using these two equations, we can solve for "r" and "c".

Expanding the first equation, we get:
24 = 4r - 4c

Expanding the second equation, we get:
18 = 3r + 3c

Now, we have a system of two equations:
4r - 4c = 24
3r + 3c = 18

We can solve this system using the method of elimination.

Multiplying the first equation by 3 and the second equation by 4, we get:
12r - 12c = 72
12r + 12c = 72

Adding the two equations together, we eliminate the "c" terms:
24r = 144

Dividing both sides by 24, we find:
r = 6

Therefore, the rate at which Laura and Brent paddled in still water is 6 miles per hour.