Alice walks along a road which can be modeled by the equation y=6x, where (0,0) represents her starting point. When she reaches a certain point A, she turns right, so that she is traveling perpendicular to the original road, until she stops at the point (333,0). What was the point A where Alice turned?

9514 1404 393

  (9, 54)

Step-by-step explanation:

The first road has a slope of 6 on its graph. So, the perpendicular road will have a slope of -1/6, the negative reciprocal of the slope of the original road. Translating that from y=-1/6x the the right by 333 units, the equation of the second road is ...

  y = -1/6(x -333)

The point where Alice turned is the point of intersection of these two equations:

Substituting for y, we have ...

  6x = -1/6(x -333)

  36x = -x +333 . . . . . multiply by 6, eliminate parentheses

  37x = 333 . . . . . . . .  add x

  x = 9 . . . . . . .  divide by 37

So, the point where Alice turned is ...

  (x, y) = (9, 6·9)

  (x, y) = (9, 54)

three-fourths of an hour

36÷48=0.75

0.75=

125 yards

step-by-step explanation:

i take 75 plus 50.