Thaddeus and lan start at the same location and drive in opposite directions, but leave at different times. when they are 365 miles apart, their combined travel is 16 hours. if thaddeus drives at a rate of 20 miles per hour and lan drives at a rate of 25 miles per hour, how long had each been driving?

thaddeus has been hours and lan has been hours.

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Step-by-step explanation:

If Thaddeus drives the whole 16 hours, the distance between them is ...

  distance = speed · time

  distance = 20 mi/h · 16 h

  distance = 320 miles.

It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...

  (45 mi)/(5 mi/h) = 9 h

The rest of the 16 hours is the time that Thaddeus drove: 7 hours.

___

Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...

  distance = speed · time

  365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)

  45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms

  (45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x

Comment on the solution

You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.

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step-by-step explanation:

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation: