anonymous
  • anonymous
Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current. 1- 7 mph 2- 3 mph 3- 2.5 mph 4- 4 mph
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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whpalmer4
  • whpalmer4
Have you done any problems like this before?
anonymous
  • anonymous
no but i try them a lot but it does not work with me
whpalmer4
  • whpalmer4
Okay, no problem. They are kind of fun once you know how to do them. Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current. Let's call the distance they row \(x\). We don't know how far it is, and it turns out not to matter. Do you know the formula to find the distance traveled if you know the speed and time?

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anonymous
  • anonymous
i know the destiny is 40 and the time is 4 and 10 but i try to do but i could not do them
anonymous
  • anonymous
d=r*t
whpalmer4
  • whpalmer4
Good. So let's call the speed of the boat in still water \(v_s\), and the speed of the current \(v_c\) When the boat goes with the current, the speed of the boat is \(v_s+v_c\) When the boat goes against the current, the speed of the boat is \(v_s - v_c\) Does that make sense?
anonymous
  • anonymous
ok
whpalmer4
  • whpalmer4
Oh, I see we DO know the distance they travel. 40 miles. Rowing downstream (with the current), \[d = r * t\]\[40 \text{ miles} = (v_s + v_c)*(4\text{ hours})\] Rowing upstream (against the current), \[d = r*t\]\[40 \text{ miles} = (v_s - v_c)*(10\text{ hours})\] For simplicity, I will drop the units and we will just remember that we are working in hours, and miles. \[40 = 4(v_s+v_c)\]\[40 = 10(v_s-v_c)\] That is a pair of equations in two unknowns. Do you know how to solve it?
anonymous
  • anonymous
not really
whpalmer4
  • whpalmer4
Well, let's start by using the distributive property to get rid of the parentheses. What do you get if you expand those two equations?
anonymous
  • anonymous
4u+4u 10u-10u
whpalmer4
  • whpalmer4
No. I will do one, you do the other. \[40 = 4(v_s+v_c)\]\[40 = 4*v_s + 4*v_c\]\[40=4v_s + 4v_c\] Now you do the other. Use vs and vc for the two variable names. \[40 = 10(v_s-v_c)\]
anonymous
  • anonymous
40=10U-10U
anonymous
  • anonymous
i do not know how to do ur U so
whpalmer4
  • whpalmer4
Those are two different variable names, maybe it is hard to see on your screen. Let me start over and we will use \(b\) for the speed of the boat in still water and \(c\) for the speed of the current. speed of boat going downstream: \(b+c\) speed of boat going upstream: \(b - c\) Is that clearer?
anonymous
  • anonymous
yes
whpalmer4
  • whpalmer4
Then we have: \[40\text{ miles} = (b+c) * 4\text{ hours}\]\[40 \text{ miles}= (b-c) * 10\text{ hours}\] or dropping the units \[40 = 4(b+c)\]\[40=10(b-c)\] Now if we expand those two: \[40 = 4b + 4c\]\[40 = 10b-10c\] Okay?
anonymous
  • anonymous
ok
whpalmer4
  • whpalmer4
That's a system of two equations in two unknowns. We can solve it by substitution or elimination. Do you know either of those methods?
anonymous
  • anonymous
80=14b-6c
whpalmer4
  • whpalmer4
Substitution might be the easiest. We take one equation, and solve it to give one variable in terms of the other. \[40 = 4b+4c\]\[40 - 4b = 4c\]\[10-b = c\]Now we take that expression for \(c\) and replace \(c\) wherever we find it in the other equation: \[40 = 10b - 10c\]\[40 = 10b - 10(10-b)\]Can you solve that equation for \(b\), please?
anonymous
  • anonymous
ok 10*40=4b+4c 4*40=10b-10c 400=40b-40c 160=40b-40c 560=80b b=7 c=3
anonymous
  • anonymous
+40c -40c
whpalmer4
  • whpalmer4
yes, b = 7 and c = 3 are correct. The boat goes 7 mph in still water, so downstream it goes 10 mph, and upstream it goes 4 mph. Let's check that with the problem: downstream we go 40 miles in 4 hours = 10 mph upstream we go 40 miles in 10 hours = 4 mph both answer check out!
anonymous
  • anonymous
only u can chose one so i will see 7
anonymous
  • anonymous
speed of the boot is 3 so 3+4=7 3-10=7
anonymous
  • anonymous
thanks buddy but i will write every word u have wrote in here thanks
anonymous
  • anonymous
but the anwser was 3 gad
whpalmer4
  • whpalmer4
No the speed of the the boat is 7, the speed of the current is 3.
whpalmer4
  • whpalmer4
b=boat c=current we got b=7, c=3
anonymous
  • anonymous
yes thanks
anonymous
  • anonymous
i am just going to write how did u do the problem so i can do it next time

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