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Kitty [74]
2 years ago
5

A marathon runner runs at the rate of 9 mph for the complete course. A track man runs at 12 mph. If together they run for 3 hrs.

, 1 min. to complete a total of 28 miles, how far did the marathon runner run? 24 3/5 miles 21 miles 20 4/5 miles
Mathematics
2 answers:
weqwewe [10]2 years ago
7 0
The first thing to do is organize all the given data so that you won't be confused which is which. Let's denote all the given that belongs to the marathon runner with a subscript of 1 and that of the trackman with a subscript of 2. The first equation we could do is find the sum of time:

t₁ + t₂ = 3 hours and 1 minute

For consistency, let's convert minute to hours. 
1 minute (1 hour/60 minutes) = 1/60
Total time = 3+1/60 = 3.0167 hours

t₁ + t₂ = 3.0167 hours  ----> equation 1

The other equation is the total distance. When you multiply speed with time, the answer would be distance. Thus.

9t₁ + 12t₂ = 28 miles ----> equation 2

Since there are two unknowns and 2 equations, the system is solvable:

t₁ = 3.0157 - t₂
9(3.0167 - t₂) + 12t₂ = 28
t₂ = 0.2832 hour, and 
t₁ = 3.0157 -  0.2832 = 2.733 hours

Therefore, the distance run by the marathon runner is
9*2.733 = 24.597 or approximately 24 3/5.
posledela2 years ago
6 0

Answer:

24 3/5

Step-by-step explanation:

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In a basketball tournament, team A scored 6 more points than 3 times as many points as team B scored. Team C scored 45 more poin
Sophie [7]
A + B + C = 476
A = 3B + 6
C = B + 45

now its just a matter of subbing..
A + B + C = 476
(3B + 6) + B + (B + 45) = 476...combine like terms
5B + 51 = 476
5B = 476 - 51
5B = 425
B = 425/5
B = 85 <== team B scored 85

A = 3B + 6
A = 3(85) + 6
A = 255 + 6
A = 261 <=== team A scored 261

C = B + 45
C = 85 + 45
C = 130 <=== team C scored 130
6 0
2 years ago
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A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?
yKpoI14uk [10]

Answer:

21/20

Step-by-step explanation:

a) One hour is equivalent to 60 minutes.

So we can multiply 50 minutes by the fraction \frac{1 hour}{60 minutes}, so we could convert 50 minutes to hours.

It is:

50 minutes * \frac{1 hour}{60 minutes}=\frac{50}{60}hours

If we simplify the fraction, we have:

50 minutes = \frac{5}{6}hours

b) In order to express the turtle's speed in miles per hour, we have to divide

\frac{7}{8}miles by  \frac{5}{6}hours

So:

\frac{\frac{7}{8}miles }{\frac{5}{6}hours }

We simplify the expression by multiplying 7 mile by 6 and 8 by 5 hours:

\frac{\frac{7}{8}miles }{\frac{5}{6}hours}=\frac{42 miles}{40 hours} =\frac{21 miles}{20 hours}

4 0
2 years ago
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Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)
nevsk [136]

Answer:

Option 1:(x-4)^2+y^2=100

Step-by-step explanation:

Given center = (h,k) = (4,0)

The point (-2,8) lies on circle which means the distance between the point and center will be equal to the radius.

So,

The distance formula will be used:

d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}} \\=\sqrt{(4+2)^{2}+(0-8)^{2}}\\=\sqrt{(6)^{2}+(-8)^{2}}\\=\sqrt{36+64}\\ =\sqrt{100}\\ =10\ units

Hence radius is 10.

The standard form of equation of circle is:

(x-h)^2+(y-k)^2 = r^2

Putting the values

(x-4)^2+(y-0)^2=10^2

(x-4)^2+y^2=100

Hence option 1 is correct ..

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2 years ago
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The diameter of Circle Q terminates on the circumference of the circle at (0,3) and (0,-4). Write the equation of the circle in
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First, determine the center of the circle by getting the midpoint of the points given for the circumference.
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Then, we get the radius by determining the distance from either of the circumferential point to the center. 
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The equation for the circle would be,
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charle [14.2K]

Answer: 2:7 is your answer

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