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Dafna11 [192]
3 years ago
6

Maury completed a bicycle race 1.5 hours faster than Vince at an average speed of 16 miles per hour. Vince completed the same ra

ce at an average speed of 12 miles per hour. How many miles was the race?
Mathematics
1 answer:
MAXImum [283]3 years ago
3 0
Let the time taken by Vince to complete the race was x hours. 
Maury completed the race 1.5 hours faster. This means Maury complete the race in (x - 1.5) hours.

Average Speed of Maury = 16 miles per hour
Average Speed of Vince = 12 miles per hour

Distance = Speed x Time.

For Maury:
Distance = 16(x - 1.5)

For Vince:
Distance = 12x

Since the distance covered by both was the same, we can equate the two equations as:

16(x - 1.5) = 12x
16x - 24 = 12x
4x = 24
x = 6 
This means Vince complete the race in 6 hours.

Distance = Speed x Time = 12 x 6 = 72 miles

Thus, the total distance of the race was 72 miles. 
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Step-by-step explanation:

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The graph of y > 1 2 x - 2 is shown. Which set contains only points that satisfy the inequality? A) {(6, 1), (-1, -3), (4, 4)
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Answer:

Option B) {(1, -1), (-3, -3), (2, 4)}

Step-by-step explanation:

<u><em>The correct inequality is </em></u>

y>\frac{1}{2}x-2

The solution of the inequality is the shaded area above the dashed line y=\frac{1}{2}x-2

see the attached figure to better understand the problem

we know that

If a ordered pair satisfy the inequality, then the ordered pair must lie in the shaded area of the solution

<u><em>Verify each case</em></u>

case A) {(6, 1), (-1, -3), (4, 4)}

ordered pair (6,1)

For x=6, y=1

substitute in the inequality

1>\frac{1}{2}(6)-2

1>1 ---> is not true

therefore

The point not satisfy the inequality

case B)  {(1, -1), (-3, -3), (2, 4)}

ordered pair (1,-1)

For x=1, y=-1

substitute in the inequality

-1>\frac{1}{2}(1)-2

-1>-1.5 ---> is true

so

The point satisfy the inequality

ordered pair (-3,3)

For x=-3, y=3

substitute in the inequality

3>\frac{1}{2}(-3)-2

3>-3.5 ---> is true

so

The point satisfy the inequality

ordered pair (2,4)

For x=2, y=4

substitute in the inequality

4>\frac{1}{2}(2)-2

4>-1 ---> is true

so

The point satisfy the inequality

therefore

The set contains only points that satisfy the inequality

case C) {(1, -1), (-3, -3), (4, -2)}

ordered pair (4,-2)

For x=4, y=-2

substitute in the inequality

-2>\frac{1}{2}(4)-2

-2>0 ---> is not true

therefore

The point not satisfy the inequality

case D) {(-1, -3), (-3, -3), (2, 4)}

ordered pair (-1,-3)

For x=-1, y=-3

substitute in the inequality

-3>\frac{1}{2}(-1)-2

-3>-2.5 ---> is not true

therefore

The point not satisfy the inequality

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Vladimir79 [104]

Answer:

Step-by-step explanation:

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x -int

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-2y = 18

y = -9

(0, -9)

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