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Lisa [10]
3 years ago
7

A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rat

e of the boat in still water.
Mathematics
1 answer:
Mandarinka [93]3 years ago
6 0
Recall your d = rt, distance = rate * time.

now, if the boat has a speed of say "b", and the current has a speed of say "c", when the boat is going upstream, is not really going "b" fast, is going " b - c " fast, because the current is eroding speed from it, going upwards.

And when the boat is going downstream, is not going "b" fast either, because the current is now adding to speed to it, so is really going " b + c " fast.

The time it took one way, is the same time it took back, 4 hours each way.

thus

\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\
&------&------&------\\
Upstream&20&b-c&4\\
Downstream&32&b+c&4
\end{array}
\\\\\\
\begin{cases}
20=4(b-c)\implies \frac{20}{4}=b-c\implies 5+c=\boxed{b}\\
32=4(b+c)\implies \frac{32}{4}=b+c\implies 8=b+c\\
--------------------\\
8=\left(\boxed{5+c}  \right)+c
\end{cases}
\\\\\\
8=5+2c\implies 3=2c\implies \cfrac{3}{2}=c\implies 1\frac{1}{2}=c

what's the speed of the boat?  well, 5 + c = b.
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Answer:

66%

Step-by-step explanation:

Given :

Age          Percentile

75           97

65           90

55           78

45           58

35           37

25           13

20           66

To Find :The percentage of drivers who are younger than 20 is _____%.

Solution:

Refer the given table

The percentile corresponding to age 20 is 66.

Percentile : A data item is said to be in nth percentile of distribution if n% of the distribution are less than that particular data item.

So, drivers who are younger than 20 are said to be in 66 percentile if 66%of the distribution are less than that particular data item.

Hence The percentage of drivers who are younger than 20 is 66%.

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En una fiesta hay 40 asistentes de los cuales el número de varones que no bailan es el doble que el número de las mujeres que no
Arte-miy333 [17]

Answer:

50%

Step-by-step explanation:

Para resolver este problema vamos a definir 4 variables:

V= número de varones bailando.

M= número de mujeres bailando.

V' = número de varones que no están bailando.

M' = número de mujeres que no están bailando.

Sabemos que hay 40 personas en la fiesta, por lo que podemos construir la siguiente ecuación:

V+M+V'+M'=40

Vamos a suponer que cada mujer que está bailando, está bailando varón respectivamente. (El problema no da más información, entonces podemos suponer esto.)

Entonces si hay 5 mujeres bailando, entonces también hay 5 hombres bailando, por lo que nuestra ecuación se reescribe de la siguiente manera:

5+5+V'+M'=40

y simplificamos:

10+V'+M'=40

V'+M'=40-10

V'+M'=30

Ahora bien, el problem nos dice que el número de varones que no bailan es el doble del número de mujeres que no bailan en un determinado momento. Entonces con esta información podemos construir la siguiente ecuación:

V'=2M'

Y podemos despejar el número de mujeres que no bailan, lo que nos da:

M'=\frac{V'}{2}

Entonces podemos sustituir esto dentro de nuestra ecuación para obtener:

\frac{V'}{2}+V'=30

y podemos entonces despejar V'

\frac{3V'}{2}=30

V'=\frac{2(30)}{3}

V'=20

Entonces hay 20 varones que no están bailando, por lo que la probabilidad de que el varón que se escoge al azar no esté bailando está dada por la siguiente fórmula:

P=\frac{V'}{total}

P=\frac{20}{40}=\frac{1}{2}

P=50%

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