Question

tracey leaves detroit at 8:00 am going 55mph, and kelly leaves at 10:00am going 65mph. when will kelley catch up with tracey

Answer 1

Give me a moment.

Answer 2

Okay. So are you ready to start solving?

Answer 3

Great. So what we want to do is solve for the time it takes. The easiest way to do this is by a table of distances. Do you know what that is?

Answer 4

No, not like that. I mean like this:

Answer 5

And then going down like that.

Answer 6

But there is a shortcut - do you want to know it?

Answer 7

Oh, that's silly. That forces you to write out too much work. But what you want to do is for T you want the amount of time since 8 o'clock and for D you just multiply R and T.

Answer 8

You still confused?

Answer 9

D = R x T.

Answer 10

Use your chart. Tracey's rate is 55, her time is t, and her distance is 55t. Kelley's rate is 65, her time is t-2, and her distance is 65(t-2). We want 55t to equal 65(t-2). Solve. Do you get it now?

Answer 11

Great.

Answer 12

What did you get?

Answer 13

Good, now keep going.

Answer 14

No, you subtract 55t from both sides and add 130 to both sides. Then you divide both sides by 10 and get t=13.

Answer 15

Not negative. Positive 13. And I would be willing to stake my life on it.

Answer 16

Points can't have x and y as their coordinates. That problem is badly written.

Answer 17

Oh, never mind, I get it. It's just \[\left| x-y \right|\]

Answer 18

No problem. A medal is more than enough! Glad to help.