I was given a problem on a test and I know the correct answer, due to the professor telling me, however I am not sure how to come about the answer... The problem is:
The speed of a stream is 6 mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles up stream, what is the speed of the boat in still water?
This problem is a bit tricky because you are asked to find one thing, but you may need to find several to find the one you want.
First step in a word problem is to assign symbols or expressions to the unknowns.
\(\displaystyle Let\ s = \text{speed of boat in still water; this is what you want to find.}\)
There is a little formula involving speed, distance and time. You have distances, but you will need to consider time.
\(\displaystyle Let\ t = \text{time for trips upstream and downstream.}\)
Second step is to put the conditions of the problem into mathematical form.
\(\displaystyle \text{Using your symbols for the unknowns, what is the speed of the boat going downstream in terms of s?}\)
\(\displaystyle \text{Using your symbols for the unknowns, what is the speed of the boat going downstream in terms of the speed, distance, time formula?}\)
This gives you an equation. What is it? Write it down.
\(\displaystyle \text{Using your symbols for the unknowns, what is the speed of the boat going upstream in terms of s?}\)
\(\displaystyle \text{Using your symbols for the unknowns, what is the speed of the boat going upstream in terms of the speed, distance, time formula?}\)
This gives you another equation. What is it? Write it down.
You now have two equations in two unknowns. Do you see how to solve them?
If so, what answer do you get and does it work when checked?
