Question 1192951
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The downstream speed is 48/4 = 12mph; the upstream speed is 48/24 = 2mph.<br>
If you need a solution using formal algebra....<br>
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)<br>
Add the two equations; variable c is eliminated;<br>
2k=14
k=7<br>
Find the speed of the current using k=7 in either of the earlier equations.<br>
7+c=12
c=5<br>
ANSWER: speed of the kayak = k=7; speed of the current = c=5<br>
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.<br>
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.<br>