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3 years ago

Sarah and four friends are decorating picture frames with ribbon. They have 4 rollsof ribbon to share evenly?

1 answer:

7 0

"Sarah and four friends", this means that we have a total of 5 persons.
They have four rolls of ribbon to share evenly.
1- This represents division as they have to equally divide four rolls among them.

2- The share of each can be calculated by dividing the four rolls they have by the five of them as follows:
share of each = 4/5 rolls = 0.8 rolls

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2 years ago

An airplane is preparing to land at an airport. It is 44,8000 feet above the ground and is descending at the rate of 3,100 feet

Marina86 [1]

Answer:

Time: 8 minutes

Altitude: 20000ft

Method 1 is easiest

Method 3 is easiest

Step-by-step explanation:

Given

Airplane 1:

$Height = 44800 ft$

$Descending\ Rate = 3100ft/min$

Airplane 2:

$Ascending\ Rate = 2500ft/min$

Required

Determine when both planes would be at the same altitude?

Let the minute be represented by m

For Airplane 1, Its altitude at any height h is:

$Airplane\ 1 = Height - Descending\ Rate * m$

It is minus (-) because the airplane is descending

$Airplane\ 1 = 44800 - 3100 * m$

$Airplane\ 1 = 44800 - 3100m$

For Airplane 2, Its altitude at any height h is:

$Airplane\ 2 = Ascending\ Rate * m$

$Airplane\ 2 = 2500 * m$

$Airplane\ 2 = 2500m$

Method 1:

For both heights to be equal, we have that:

$Airplane\ 1 = Airplane\ 2$

This gives:

$44800 - 3100m = 2500m$

Collect Like Terms

$44800 = 2500m + 3100m$

$44800 = 5600m$

$5600m = 44800$

$m = 44800/5600$

$m = 8\ min$

Hence, the time they will be at the same altitude is 8 minutes

Substitute 8 for m in

$Airplane\ 2 = 2500m$

$Airplane\ 2 = 2500 * 8$

$Airplane\ 2 = 20000\ ft$

Hence, they will be at the same altitude at 20000ft

Method 2:

We have that:

$Airplane\ 1 = 44800 - 3100m$

$Airplane\ 2 = 2500m$

Since they are to be at the same altitude, then

The difference in their altitude must be 0

i.e.

$Airplane\ 1 - Airplane\ 2 = 0$

This gives

$44800 - 3100m - 2500m = 0$

$44800 - 5600m = 0$

Collect Like Terms

$5600m = 44800$

$m = 44800/5600$

$m = 8\ min$

Substitute 8 for m in

$Airplane\ 1 = 44800 - 3100m$

$Airplane\ 1 = 44800 - 3100 * 8$

$Airplane\ 1 = 44800 - 24800$

$Airplane\ 1 = 20000\ ft$

Method 3:

We have that:

$Airplane\ 1 = 44800 - 3100m$

$Airplane\ 2 = 2500m$

Since they are to be at the same altitude, then

The ratio of their altitudes must be 1

i.e.

$\frac{Airplane\ 1}{Airplane\ 2} = 1$

$\frac{44800 - 3100m}{2500m} = 1$

Cross Multiply

$44800 - 3100m = 1 * 2500m$

$44800 - 3100m = 2500m$

Collect Like Terms

$44800 = 2500m + 3100m$

$44800 = 5600m$

$5600m = 44800$

$m = 44800/5600$

$m = 8\ min$

Substitute 8 for m in

$Airplane\ 1 = 44800 - 3100m$

$Airplane\ 1 = 44800 - 3100 * 8$

$Airplane\ 1 = 44800 - 24800$

$Airplane\ 1 = 20000\ ft$

Hence;

Their altitudes must be 20000ft

Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.

Method 3 is the most difficult.

7 0

3 years ago