freemap
  • freemap
3. When a boat traveled downstream from Town A to Town B, the trip took 3 h. When the same boat traveled upstream from Town B to Town A, the trip took 3.6 h. For each trip, the speed of the boat and the water current were unchanged. Let x represent the speed of the boat and let y represent the speed of the water.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
freemap
  • freemap
(a) Write an expression for the distance traveled downstream using 3 h for the time. Then write an expression for the distance traveled upstream using 3.6 h for the time. (b) Set the expressions in Part (a) equal to each other. Then solve the equation for y. Show your work. (c) What percent of the boat’s speed is the water current?
phi
  • phi
have you learned rate * time = distance or speed * time = distance or velocity * time = distance ?
freemap
  • freemap
yes I have

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More answers

phi
  • phi
For traveled downstream first, what is the speed of the boat going with the current?
freemap
  • freemap
I don't remember how to do this. I'm I suppose to multiply?
phi
  • phi
The only reason people study math is to give them an excuse to think (or puzzle out a problem) Say you were in a canoe but did not paddle, and drifted downstream. According to the info in this problem, how fast will you be moving ?
freemap
  • freemap
Umm I really don't mean to sound stupid, but 1 maybe. not very fast
phi
  • phi
you will be going at a speed of "y" (they tell us let y represent the speed of the water.)
phi
  • phi
though y is a letter, it means "speed of the current" (it's short-hand)
phi
  • phi
If you start paddling you will go faster. You would add on the speed you can paddle they say Let x represent the speed of the boat (when paddling in still water) do you know how to show x added to y ?
freemap
  • freemap
hmm y+ x+y?
phi
  • phi
just x+y that is how fast you go if you go downstream we might want to put parens around it , so we remember it as one thing: speed of the boat: (x+y) now we use speed * time = distance (x+y)* time = distance they don't tell us the distance, we let's call the distance "d" but we know the time. can you fill in the time with a number and write the full equation?
freemap
  • freemap
(x+y)*1=d
phi
  • phi
looks good, except why are you using 1 for the time ? what does the question say the time is for going downstream ?
freemap
  • freemap
(x+y)*3.6h=d
phi
  • phi
Write an expression for the distance traveled downstream using 3 h for the time.
freemap
  • freemap
(x+y)*3h=d
phi
  • phi
ok. I think the h mean hours. Probably we should leave it off. so (x+y)*3 = d or 3(x+y)= d is the answer to the first part.
phi
  • phi
now you need to the speed going upstream any ideas ?
freemap
  • freemap
(x+y)*3.6=d or 3.6(x+y)=d
phi
  • phi
(x+y) is how fast you go downstream when you go upstream, you go slower
freemap
  • freemap
would it be x-y
phi
  • phi
the river is taking you backwards at a speed of y , as you paddle upriver at a speed of x yes (x-y) is the speed going upstream
freemap
  • freemap
ok would we still multiply the time like (x-y)*3.6=d
phi
  • phi
yes, exactly. now you have part a) 3(x+y)= d 3.6(x-y) = d
phi
  • phi
now ***Set the expressions in Part (a) equal to each other. Then solve the equation for y. Show your work. *** we see that 3(x+y) = d and 3.6(x-y) also equals d. if both are equal to d, we can say 3(x+y)= 3.6(x-y) Does that make sense ?
freemap
  • freemap
It does make since d is the outcome in both equations
freemap
  • freemap
expressions i mean
phi
  • phi
to solve, distribute the 3 on the left side. that means multiply 3 times x and times y ditto for the 3.6 on the other side
freemap
  • freemap
ok 3x+3y=3.6x-3.6y do we then add like terms?
phi
  • phi
yes,
phi
  • phi
3x+3y=3.6x-3.6y I would add 3.6y to both sides 3x + 3y + 3.6y = 3.6x -3.6y +3.6y
phi
  • phi
you get 3x+6.6y = 3.6x now add -3x to both sides
freemap
  • freemap
6.6y=-0.833
phi
  • phi
you lost the x? what is 3.6x - 3x ?
freemap
  • freemap
0.6x
phi
  • phi
yes, so you get 3x+6.6y = 3.6x 6.6y = 0.6 x now divide both sides by 6.6 what do we get ?
freemap
  • freemap
11
phi
  • phi
you get \[ y= \frac{0.6}{6.6} x\] that simplifies to \[ y = \frac{1}{11} x \]
freemap
  • freemap
Ok I get it
phi
  • phi
**(c) What percent of the boat’s speed is the water current? *** I would find the ratio of y/x and change it to a percent. of course, we can't use just "y", but we know y is the same as x/11 so use x/11 instead. can you do that ?
phi
  • phi
you do \[ \frac{y}{x}= y \cdot \frac{1}{x} \] but y is x/11 so \[ \frac{y}{x}= \frac{x}{11} \cdot \frac{1}{x} \]
freemap
  • freemap
ok, so if i multiply it turns back into 1x and 11x so I'm really sure how to solve this
phi
  • phi
you should learn that if you have the same thing "up top" and "below" , they cancel when you multiply fractions, you multiply top times top and bottom times bottom \[ \frac{x \cdot 1 }{11 \cdot x}\] as you know we can change the order of the multiply (right ?) so it's the same as \[ \frac{1 \cdot x }{11 \cdot x}\] but that is the same as multiplying the two fractions \[ \frac{1 \cdot x }{11 \cdot x} = \frac{1}{11} \cdot \frac{x}{x}\]
phi
  • phi
the last step, we "undid" the multiply the point is, we have x/x and anything divided by itself is 1 in other words we get \[ \frac{1}{11} \cdot 1 = \frac{1}{11} \]
phi
  • phi
that is the long way. the short way is to say "x up top, x down below" cross off both \[ \frac{y}{x}= \frac{\cancel{x}}{11} \cdot \frac{1}{\cancel{x}} = \frac{1}{11}\]
freemap
  • freemap
Thats what I meant to say 1/11 because I did cross multiply
phi
  • phi
no, you should not cross multiply. Try to follow what I posted up above. meanwhile, to answer the question, change 1/11 to a decimal, and then multiply by 100 to make it a percent.
freemap
  • freemap
ok, 0.11
phi
  • phi
0.11 means 11/100 that is different from 1/11 to change it to a decimal, divide 11 into 1 (a calculator will do that) or type 1/11= into google
freemap
  • freemap
9.09 after multiplying 100
phi
  • phi
and add a % sign (which is how we show we multiplied by 100) 9.09%
freemap
  • freemap
9.09% got it
freemap
  • freemap
Thank you so very much. I really appreciate your help.

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