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vredina [299]
3 years ago
12

At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the sam

e distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
Mathematics
1 answer:
nikdorinn [45]3 years ago
7 0
Let x the maximum speed of the plane and y be the speed of the wind.

We know that:
1)Distance = speed x time
2) if the head wind is y, then the resulting speed is x-y (against the wind)
3) if the tail wind is y, then the resulting speed is x+y (with the wind)

1) and 2): 2400 = (x-y).(6) or 6x-6y = 2400

1) and 3): 2400 = (x+y).(5) or 5x+5y = 2400

Hence the system of 2 equation:

6x - 6y = 2400
5x + 5y = 2400.
Solving it gives  x = 440 mi/h and y = 40 mil/h
Then the speed of the plane with no wind is 440 km/h

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A recipe for 12 waffles calls for 112 cups of milk, 214 cups of flour, and 113 cups of other ingredients. 4 pts each/16 pts tota
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This question was not written properly

Complete Question

A recipe for 12 waffles calls for 1 1/2 cups of milk, 2 1/4 cups of flour, and 1 1/3 cups of other ingredients.

Answer:

A 5 1/12 cups of ingredients

B 10 1/6 cups of ingredients

C The total amount of ingredients for 12 waffles would increase from the original recipe.

D 7.56 or 7 5/9 recipes

Step-by-step explanation:

A... What is the total number of cups of ingredients needed for 12 waffles?...

The total number of cups of ingredients needed =

1 1/2 cups of milk + 2 1/4 cups of flour + 1 1/3 cups of other ingredients

(1 + 2 + 1) + (1/2 + 1/4 +1/3)

4 + ( 6 + 3 + 4/12)

4 + (13/12)

4 + (1 1/12)

= 5 1/12 cups of ingredients

B... What is the total number of cups of ingredients needed for 36 waffles? ....

If 12 waffles requires = 5 1/12 cups of ingredients

36 waffles =

Cross Multiply

= (36 waffles × 5 1 /12)/12 waffles

= 10 1/6 cups of ingredients

C... If the milk is reduced to 1 cup and the amount of 'other ingredients' (not including the flour) is increased to 2 cups, would the total amount of ingredients for 12 waffles increase or decrease from the original recipe?

Justify your thinking...

Original recipe.

A recipe for 12 waffles calls for 1 1/2 cups of milk, 2 1/4 cups of flour, and 1 1/3 cups of other ingredients = total of 5 1/12 cups of ingredients

Current recipe

1 cup of milk + 2 1/4 cups of flour + 2 cups of other ingredients

1 + 2 + 2 + (1/4)

5 1/4 cups of ingredients

Therefore, total amount of ingredients for 12 waffles would increase from the original recipe. This is because when you subtract 5 1/12 from 5 1/4 you get a difference of 1/6 cups

5 1/4 - 5 1/12 = 1/6

D... If a baker has a 5 pound bag of flour, which is approximately 17 cups of flour, how many complete recipes for 12 waffles can the baker make?... Justify your thinking...

The original recipe has 2 1/4 cups of flour as its quantity for 12 waffles

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2 1/4 cups of flour = 12 waffles

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17 × 12/2 1/4

= 204÷ 2 1/4

= 204 ÷ 9/4

= 204 × 4/9

= 90.666666667 or 90 2/3 Waffles

If = 12 waffles = 1 recipe

90 2/3 waffles =

7.56 or 7 5/9 recipes

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