During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream (with the current). The speed of the current remained constant during the trip. It took the kayaker 3 hours to travel upstream and 2 hours to travel downstream.
A) set up a system of equations to represent this situation
B) solve the system of equations to find the average speed of a kayak in still water and speed of the current. Make sure you label the speed of a kayak in still water and the speed of the current.
Speed of kayaker in still water : x mph
speed of current : y mph
time to upstream = 12/(x-y)
time to go downstream = 12/(x+y)
12/(x-y) = 3
3x - 3y = 12
x - y = 4 , #1
12/(x+y) = 2
2x + 2y = 12
x + y = 6, #2
add #1 and #2,
2x = 10
pick it up from here
A) To set up a system of equations to represent this situation, we can use the following variables:
Let's denote the speed of the kayak in still water as "k" (in miles per hour).
Let's denote the speed of the current as "c" (in miles per hour).
For the upstream trip:
Distance = Speed × Time
Distance = (k - c) × 3 (Since the kayak is going against the current, its effective speed is k - c)
Distance = 3k - 3c
For the downstream trip:
Distance = Speed × Time
Distance = (k + c) × 2 (Since the kayak is going with the current, its effective speed is k + c)
Distance = 2k + 2c
B) Now, let's solve this system of equations to find the average speed of the kayak in still water (k) and the speed of the current (c).
From equation 1: 3k - 3c = 12
Divide both sides of the equation by 3:
k - c = 4
From equation 2: 2k + 2c = 12
Divide both sides of the equation by 2:
k + c = 6
Now, we have a system of equations:
k - c = 4
k + c = 6
We can solve this system of equations using the method of addition or elimination.
Let's add the two equations together:
(k - c) + (k + c) = 4 + 6
2k = 10
Divide both sides by 2:
k = 5
Now substitute the value of k into either of the original equations, such as k + c = 6:
5 + c = 6
c = 6 - 5
c = 1
Therefore, the average speed of the kayak in still water is 5 miles per hour, and the speed of the current is 1 mile per hour.