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4 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?

1 answer:

madam [21]4 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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Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster tha

lara31 [8.8K]

Answer:

Step-by-step explanation:

Given as :

The distance cover while running = $D_1$ = 5 miles

Let The speed for running = $S_1$

The distance cover with bike = $D_2$ = 80 miles

The speed for biking = $S_2$ = 15 mph + $S_1$

Total Time taken = 5 hours

Now Time = $\dfrac{\textrm Distance}{\textrm Speed}$

∴ 5 hour = $\frac{D_1}{S_1}$ + $\frac{D_2}{S_2}$

Or, 5 hour = $\frac{5}{S_1}$ + $\frac{80}{15+S_1}$

Or, 5 hour = $\frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}$

or, 5 × ( $S_1^{2}+15 S_1$ ) = $85 S_1 + 75$

Or, $5 S_1^{2} + 75 S_1$ - $85 S_1 - 75$ = 0

or, $5 S_1^{2} -10 S_1 - 75$ = 0

or, $S_1^{2} -2 S_1 - 15$ = 0

Or, $S_1^{2} -3 S_1 + 5 S_1- 15$ = 0

Or, $S_1 (S_1 - 3) + 5 (S_1 - 3)$ = 0

Or, $(S_1 - 3) ( S_1 + 5 )$ = 0

∴ $S_1$ = 3 , - 5

So, the running speed = 3 mile per hour

And the biking speed = 15 mph + 3 mph = 18 mile per hour

Hence The running speed of Stu is 3 mile per hour . Answer

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3 years ago

x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth

daser333 [38]

9514 1404 393

Answer:

x ≈ 2.87

Step-by-step explanation:

We can subtract 6 to put the equation into a form easily solved.

x^2 +2x +1 = 15

(x +1)^2 = 15

x +1 = √15 . . . . . for the greatest solution, we only need the positive root

x = √15 -1 ≈ 2.87

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3 years ago

Which of the following describes how to read the decimal number 0.263?

Natalija [7]

Answer:

0.263

Step-by-step explanation:

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3 years ago

.A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and

Leni [432]

Answer:

a) Null hypothesis: $\mu \leq 120$

Alternative hypothesis: $\mu > 120$

b) $t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236$

The degrees of freedom are given by:

$df = n-1 = 80-1=79$

The p value for this case taking in count the alternative hypothesis would be:

$p_v =P(t_{79}>2.236)=0.0141$

Step-by-step explanation:

Information given

$\bar X=130$ represent the sample mean for the amount spent each shopper

$s=40$ represent the sample standard deviation

$n=80$ sample size

$\mu_o =120$ represent the value to verify

t would represent the statistic

$p_v$ represent the p value f

Part a

We want to verify if the shoppers participating in the loyalty program spent more on average than typical shoppers, the system of hypothesis would be:

Null hypothesis: $\mu \leq 120$

Alternative hypothesis: $\mu > 120$

The statistic for this case would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236$

The degrees of freedom are given by:

$df = n-1 = 80-1=79$

The p value for this case taking in count the alternative hypothesis would be:

$p_v =P(t_{79}>2.236)=0.0141$

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3 years ago

What is the domain of this function?<br> (0, 2), (1, 3), (2, 4), (3, 5), (4, 6)

astraxan [27]

Answer:

{0, 1, 2, 3, 4}

Step-by-step explanation:

The first number in each ordered pair, is the domain.

Hope it helps!

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3 years ago

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