Question 107494This question is from textbook Intermediate Algebra
: The speed of a boat in still water is 24 mph. If the boat travels 54 miles upstream in the same time it takes to travel 90 miles downstream, find the speed of the current.
This question is from textbook Intermediate Algebra
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! The basic formula you need to work this problem is the standard relationship between distance, rate, and time, or:
One interesting part of this particular problem is that we need to develop an expression for the rate in terms of the boat speed in still water and the speed of the current we are trying to find.
Another thing we have to recognize is that the times for both the upstream and downstream trips are equal. First let's examine the upstream trip:
 , where c is the speed of the current. Notice the minus sign because we are going against the current. Then:
For the downstream trip:
 Notice the positive sign because we are going with the current. Then:
Now, since the times for the two trips are equal, we can set the right-hand sides of our two equations equal to each other, thus:
Which looks kind of ugly, but really not that bad. Remember how we solve things that look like  by cross multiplying?
Same thing here:
And the current is 6 miles per hour.
To check the answer, just use the 6 miles per hour current speed and the 24 miles per hour boat speed to calculate the upstream (18 mph) and downstream (30 mph) speeds, then plug that into the:
 relationship to see that the times are equal.
 , Check!
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