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natita [175]
3 years ago
5

A plane is traveling 600 miles. It takes the plane 5 hours against the wind and 4 hours with the wind. What is the speed of the

plane in still air, and what is the speed of the wind?
Mathematics
1 answer:
madam [21]3 years ago
6 0

Answer: the speed of the plane in still air is 135 miles per hour

the speed of the wind is 15 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane in still air

Let y represent the speed of the wind.

The distance travelled by the plane is 600 miles.

Distance travelled = speed × time

It takes the plane 5 hours against the wind. This means that the total speed is (x-y) miles per hour. Therefore,

600 = 5(x- y) = 5x - 5y - - - - - - - 1

It takes the plane 4 hours with the wind. This means that the total speed is (x+y) miles per hour. Therefore,

600 = 4(x+ y) = 4x + 4y - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

2400 = 20x - 20y

3000 = 20x + 20y

Adding both equations

5400 = 40x

x = 5400/40 = 135

Substituting x = 135 into equation 1, it becomes

4 × 135 + 4y = 600

540 + 4y = 600

4y = 600 - 540 = 60

y = 60/4 = 15

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Mars2501 [29]

Answer:

1.2 cups

Step-by-step explanation:

6 cups / 5 batches = 1.2 cups/batch

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2 years ago
A total of tickets were sold for the school play. They were either adult tickets or student tickets. The number of student ticke
PSYCHO15rus [73]

Answer:

the number of adult ticket sold is 107 tickets

Step-by-step explanation:

The computation of the number of adult ticket sold is shown below:

Let us assume the number of tickets be x,

So, the adult be x

And for student it would be 3x

Students= 2x

Adults= x

Total = 4x

Now the equation could be

4x = 428

x = 107

This x signifies the adult tickets sold i.e 107

Hence, the number of adult ticket sold is 107 tickets

4 0
3 years ago
Amy's banana bread recipe calls for 3/4 cup of brown sugar. She only has a 1/8 cup measure. Which equivalent fraction shows the
ki77a [65]
You convert 3/4 into 8ths and that would be 6/8. so you do 1/8+5/8=6/8 so 5/8 is your answers. 
6 0
3 years ago
Read 2 more answers
What should I fill the blanks with?
Dmitriy789 [7]

Answer:

The three angles form a "linear triplet" ,  so their measures must add up to 180^o

Step-by-step explanation:

Notice that the three angles add up to cover half a circle (therefore 180 degrees of angle. Such type of angle combination is called a "linear triplet" since they add up to give a straight line.

5 0
2 years ago
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Businesses deposit large sums of money into bank accountsImagine an account with $10 million dollars in it.
adoni [48]

again, let's assume daily compounding means 365 days per year.

~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (10000000)(0.0212)(1)\implies \boxed{I=212000}

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &1 \end{cases}

A=10000000\left(1+\frac{0.0212}{365}\right)^{365\cdot 1}\implies A\approx 10214256.88 \\\\\\ \underset{\textit{earned interest amount}}{10214256.88~~ - ~~10000000 ~~ \approx ~~ \boxed{214256.88}}

what's their difference?  well

\stackrel{\textit{compounded daily}}{\approx 214256.88}~~ - ~~\stackrel{\textit{simple interest}}{212000}\implies \boxed{2256.88}

7 0
1 year ago
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