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Likurg_2 [28]
2 years ago
12

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all

the way around the pool. The total area of the deck is 456 square feet. How wide is the deck around the pool?
Mathematics
1 answer:
rodikova [14]2 years ago
4 0

Answer:

  3 feet

Step-by-step explanation:

Let x represent the width of the deck. The deck adds to the pool dimensions on both sides, so the area of the site including pool and deck will be ...

  A = (20 +2x)(50 +2x) = 1000 +140x +4x^2

The area of the pool alone is

  A = (20)(50) = 1000

So, the area of the deck is the difference:

  456 = (4x^2 +140x +1000) -(1000)

Dividing by 4 and subtracting 114, we have ...

  x^2 +35x -114 = 0

  (x -3)(x +38) = 0

Solutions to this are x = 3 and x = -38. The positive solution is the one of interest.

The deck is 3 feet wide.

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Will it cost more to rent from Company A or Company B if "Ali" rents the bounce house for 3 hours? 5 hours? 10 hours?
a_sh-v [17]

Answer:

3 HOURS : company A costs more

5 HOURS : Cost is the same

10 HOURS : Company B costs more

Step-by-step explanation:

Company A :

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Company B:

Hourly rate = $40

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prohojiy [21]

Answers:

  • slower train = 139 km per hour
  • faster train = 159 km per hour

=================================================

Explanation:

x = rate of the slower train

x+20 = rate of the faster train

rates are in km per hour, abbreviated as kph

The train traveling at x kph will travel 5x km after 5 hours.

Use this formula

distance = rate*time

Using that same formula, the faster train travels 5(x+20) = 5x+100 kilometers in 5 hours.

The two distances must add to 1490 if we want the trains to pass by each other. Assume that the trains are traveling on parallel side-by-side tracks.

--------------------------

So,

(slower train distance) + (faster train distance) = 1490

(5x) + (5x+100) = 1490

10x+100 = 1490

10x = 1490-100

10x = 1390

x = 1390/10

x = 139

The slower train moves at a rate of 139 km per hour.

x+20 = 139+20 = 159

The faster train moves at a speed of 159 km per hour.

--------------------------

Check:

The slower train travels 139 kph and travels for 5 hours, so it covers a distance of 139*5 = 695 km

The faster train has a speed of 159 kph and travels for 5 hours, so it covers 159*5 = 795 km

Total distance = 695+795 = 1490

The answers are confirmed.

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