Question 1192951: A kayak can travel 48 miles downstream in 4 hours, while it would take 24 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water, and let c represent the speed of the current.
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39620)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! A kayak can travel 48 miles downstream in 4 hours, while it would take 24 hours to make the same trip upstream.
Find the speed of the kayak in still water, as well as the speed of the current.
Let k represent the speed of the kayak in still water, and let c represent the speed of the current.
Write a distance equation for each way, dist = time * speed
4k + 4c = 48
and
24k - 24c = 48
simplify, divide by6
4k - 4k = 8
:
Add these two equation
4k + 4c = 48
4k - 4c = 8
----------------addition eliminates c, find k
8k + 0 = 56
k = 56/8
k = 7 mph is speed of the kayak in still water
then using the first equation and k=7
4(7) + 4c = 48
28 + 4c = 48
4c = 48 - 28
4c = 20
c = 20/4
c = 5 mph is the rate of the current
:
:
Check this in the original 2nd equation
24(7) - 24(5) =
168 - 120 = 48
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The downstream speed is 48/4 = 12mph; the upstream speed is 48/24 = 2mph.
If you need a solution using formal algebra....
k+c=12 (downstream, the current speed adds to the speed of the kayak)
k-c=2 (upstream, the current speed subtracts from the speed of the kayak)
Add the two equations; variable c is eliminated;
2k=14
k=7
Find the speed of the current using k=7 in either of the earlier equations.
7+c=12
c=5
ANSWER: speed of the kayak = k=7; speed of the current = c=5
There are a huge number of problems where you end up with (or are given at the beginning) the fact that the sum of two numbers is A and their difference is B. In any case like that, one of the numbers is the average of A and B; and the other is the difference between that average and either of the numbers.
In this example, with the sum of the two speeds being 12 and the difference being 2, one of the numbers is the average of 12 and 2, which is 7; and the other number is the difference between 7 and 12 (or between 7 and 2), which is 5. So the kayak speed is 7mph and the current speed is 5mph.
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