[From 10$/Pg] Crew Rowed 12 Miles
]we will be solving problems in Real Life by using the methods learned in week 4 for solving systems of equations. Most everyone has a fear of word problems because you haven’t had much experience in solving them. If you just take them one step at a time, you will find them manageable and build your confidence in your ability to successfully tackle any word problem you meet.
Remember: I am here to help you!
Please read the prompt above to see additional instructions for your Initial Post.
Here is an example to get us started. I am working out the entire problem for you, but in your initial post you only need to set up the situation and leave solving the problem to a classmate (see prompt given above).
APPLICATION PROBLEM: DISTANCE = RATE X TIME A boat’s crew rowed 12 miles downstream, with the current, in 1.5 hours. The return trip, against the current, covered the same distance but took 4 hours. Find the crews rowing rate in still water and the rate of the current.
The relationship we need to use is Distance = Rate x Time. We will have two equations: one for the trip downstream and one for the trip upstream. We have two variables: crews rowing rate in still water and rate of the current.
Let w = crews rowing rate in still water
Let c = rate of the current
Downstream: Distance = Rate x Time Rate will be w+c (rate in still water + current)
(1) 12 = (w+c) 1.5 = 1.5w+1.5c
Upstream: Distance = Rate x Time Rate will be w-c (rate in still water – current)
(2) 12 = (w-c) 4 = 4w-4c
One approach is to simplify the equations before solving the system.
(1) 12=1.5w+1.5c divide both sides by 1.5
8 = w + c
(2) 12 = 4w=4c divide both sides by 4
3 = w – c
Use Elimination on the two equations 8 = w+c
3 = w-c After adding the two equations we have 11 = 2w divide by 2
w = 11/2 = 5.5 Use this value to solve for c.
w+c = 8
5.5+c = 8
c = 8 – 5.5
Therefore, the rate of the current is 2.5 and the rate of the crew rowing in still water is 5.5. I can’t wait to see your posts. You may use a scholarly resource, just remember to cite it.