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4 years ago

The speed of a boat in still water is 50km/h. It takes the same time for the boat to

1 answer:

3 0

The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.

upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s

downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s

time (t) = x/u = y/d

10/(50-s) = 20/(50+s)

10(50+s) = 20(50-s)

500 + 10s = 1000 - 20s

30s = 500

stream speed (s) = 500/30 = 16.6 km/h

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At a special sale, all pens are sold at one price and all pencils at another price.If 3 pens and 2 pencils are sold for 47 cents

mezya [45]

3 pen + 2 pencil = .47
2 pen + 3 pencil = .38

2(3pen + 2 pencil = .47)
-3(2pen + 3 pencil = .38)

6 pen + 4 pencil = .94
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- 5 pencil = -.2
pencil = .04

3pen + 2(.04) = .47
3pen + .08 = .47
3 pen + .08 - .08 = .47 -.08
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pen = .13

Pen = 13 cents and pencil = 4 cents

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3 years ago

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3 years ago

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iogann1982 [59]

Answer:

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2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=y%20%3D%20%20-%20x%20%2B%2010%20%5C%5C%20y%20%3D%20x%20%2B%202" id="TexFormula1" title="y = -

Zepler [3.9K]

The two ys must be the same. Equate the two right hand sides.

-x + 10 = x + 2 add x to both sides.
10 = x + x + 2
10 = 2x + 2 Subtract 2 from both sides.
8 = 2x Divide by 2
x = 8/2
x = 4

Now solve for y
y = x + 2
y = 4 + 2
y = 6

Use the other equation to check it.

y = - x + 10
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4 years ago

A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the

Kay [80]

Answer: The required number of quarters in the collection is 11.

Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.

Then, according to the given information, we have

$x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

$(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Comparing the values of y from equations (iv) and (v), we get

$47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.$

Thus, the required number of quarters in the collection is 11.

7 0

3 years ago