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Yakvenalex
1 month 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:
lawyer [12.5K]1 month ago
7 0
To start, it’s important to arrange all the data provided to avoid any confusion. We will mark the marathon runner's information with a subscript of 1 and the trackman's data with a subscript of 2. Our first step will involve calculating the total time:

t₁ + t₂ = 3 hours and 1 minute

To maintain uniformity, we need to convert the minute into hours. 
1 minute (1 hour/60 minutes) = 1/60
Total time therefore equals 3 + 1/60 = 3.0167 hours

So, we have the equation: t₁ + t₂ = 3.0167 hours ----> equation 1

Next, we establish the equation for the total distance, which arises from multiplying speed by time to yield distance. Hence, we get:

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

With two unknowns and two equations, we can solve the system:

t₁ = 3.0157 - t₂
Substituting into the second equation gives us 9(3.0167 - t₂) + 12t₂ = 28
Thus, we find t₂ = 0.2832 hour, and 
t₁ = 3.0157 - 0.2832 = 2.733 hours

Consequently, the distance covered by the marathon runner would be
9*2.733 = 24.597 or roughly 24 3/5.
Svet_ta [12.7K]1 month ago
6 0

Result:

24 3/5

Detailed explanation:

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<span>A table representing a function is provided below.
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According to the data in the table, from x = 2, the value of y can be represented as
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The area calculation for the shaded section, as seen in the attached diagram, involves subtracting the area of the kite from that of the rectangle. The area of the rectangle is calculated as (3x+x)*(x+x), which simplifies to 4x*2x, equating to 8x². The area of the kite is determined using the formula (1/2)*[d1*d2], where d1 and d2 represent the diagonals, specifically d1=4x and d2=2x. Therefore, the area of the kite becomes (1/2)*[4x*2x], leading to 4x². Consequently, the area of the shaded region can be computed as 8x²-4x², resulting in 4x². Thus, the solution is 4x².
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Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc
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To address this problem, let's start by formulating the general motion equation along the vertical direction.

This gives us:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

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  • h0: starting height

For the first individual:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second individual:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

When both individuals reach the identical altitude, the following holds:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rearranging results in:

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Result:

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