Question

A bug is moving along the line 12x + 5y = 60 with constant speed 5 units per second. It crosses the x-axis when t = 0 seconds and crosses the y-axis later. When? What vector represents the movement of the bug each second?

Answer 1

@agent0smith

Answer 2

@SolomonZelman @mathstudent55

Answer 3

First draw a graph cos that'll help.

Find the slope, draw a triangle, make the hypotenuse 5. Then you can use the slope to write expressions for the other sides.

Answer 4

The slope is -12/5. Why would the hypotenuse be 5?

Answer 5

Wouldn't it be 13?

Answer 6

Would it be correct that the bug crosses the y-axis when t=1?

Answer 7

y = 12 - (12/5)x

Solving for the x-axis
0 = 12 - (12/5)x
-12 = -(12/5)x
5 = x

When t = 0, the bug crosses (5,0)

Solving for the y-axis
y = 12 - (12/5)(0)
y = 12

(5,0)
(0,12)

x = 5 - 5t
y = 12t

When x=0 then it crosses the y-axis
0 = 5 - 5t
-5 = -5t
1 = t

When t=1, the bug crosses the y-axis?

Answer 8

That doesn't look right. It travelled 13 units in 1 second.

See my above post to work out speed.