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max2010maxim [7]
3 years ago
8

When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times sl

ower than Max on his hoverboard. They took off on hoverboards at the same time, but after 12 minutes, Victoria’s hoverboard broke and she immediately started to run. If the race was a tie, how long, in minutes, did it last from start to finish?
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
5 0
<h2>Answer:</h2>

The time will be 48 minutes

<h2>Step-by-step explanation:</h2>

Let r be Max's rate of speed and t be the total time.

Using the equation d = rt for this situation

Victoria is 3 times as fast as Max so her part gives us the expression 3r(12)

For the remaining part of the race, Victoria is 3 times slower than Max.  Lets represent it as 1/3r.  Since we do not know the amount of time she travels this way so we will represent this as 1/3r(t-12)

Together the distance on hoverboard and the distance on foot can be represented by d=3r(12)+1/3r(t-12).

So we have

3r(12)+1/3r(t-12) = rt

Simplifying, we have

36r+1/3r(t)-1/3r(12) = rt

36r + 1/3rt - 12/3r = rt

36r + 1/3rt - 4r = rt

Combining all the like terms,

32r + 1/3rt = rt

Subtract 1/3rt from each side:

32r + 1/3rt - 1/3rt = rt - 1/3rt

32r = 2/3rt

Divide both sides by r we get

32r/r = (2/3rt)/r

32 = 2/3t

Divide both sides by 2/3 we get

32 ÷ 2/3 = 2/3t ÷ 2/3

32 ÷ 2/3 = t

32/1 × 3/2 = t

96/2 = t

<h2> 48 = t</h2>
NARA [144]3 years ago
4 0

Answer:

Race completed in 48 minutes.

Step-by-step explanation:

Let the speed of Max on hoverboard is = x

Then as per question speed of Victoria on hoverboard = 3x

Now it has been given in the question that speed of Victoria on foot is 1/3 of the speed of Max on hoverboard that will be = x/3

Now we will form the equation.

As we know the formula speed = distance/time

Let the time taken by both to complete the race be t minutes.

Distance covered by Victoria in 12 minutes + Distance covered by Victoria on foot = distance covered by Max on hoverboard

Then the equation will be

12(3x)+(1/3)x(t-12)=xt

36x+\frac{xt}{3}-4x=xt

x(36+\frac{t}{3}-4)=xt

36+\frac{t}{3}-4=t

32=t-\frac{t}{3}

\frac{2t}{3}=32

t=\frac{(32)3}{2}=48

So 48 minutes it took to complete the race.

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7 0
3 years ago
Question 1
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Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

                               = (Area of the rectangle + Area of the trapezoid)× depth  

Area of the trapezoid = \frac{1}{2}(b_{1}+b_{2})\times h

                                    = \frac{1}{2}(11+9)\times (12-1.5)

                                    = 105 ft²

Area of the rectangle = Length × width

                                    = 11 × 1.5

                                    = 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

                                          = 121.5 × 4

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b). Liner required = surface area of the pool excluding top

                             = Surface area of the walls + Area of the pool base

                             = (Perimeter of the pool) × depth + area of the base

                             = (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

                             = 176.8 + 121.5

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Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet                                  

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