Question

Question #fe8f6

Answer 1

Jeffrey and Marcus would have passed each other after `2.5` hours at 11:45 AM.

Explanation:

One way to picture this is by looking at the distance between Jeffrey and Marcus at some elapsed time in hours, `t`.

Start with 410 (km).

`410`

For every hour that passes, Jeffrey is closing this distance between him an Marcus by `color(red)80` km/h.

`410 - color(red)80t`

On the other side, however, Marcus is closing this distance between himself and Jeffrey by `color(blue)120` km/h, but only after 45 minutes, or `color(green)(3/4)` hours.

`410 - color(red)80t - color(blue)120(t - color(green)(3/4))`

This may also be thought of as "offsetting" the time Marcus has spent travelling by 45 minutes.

Now, the question has boiled down to finding a value of `t`, for which the distance between Jeffrey and Marcus is `color(purple)0`.

`color(purple)0 = 410 - color(red)80t - color(blue)120(t - color(green)(3/4))`

`0 = 410 - 80t - 120t + 90`

`0 = 500 - 200t`

`200t = 500`

`t = 5/2`

Finally, we need to add this time to 9:15 AM.

`5/2 = 2 1/2`

The time elapsed was `2 1/2` hours or `2` hours and `30` minutes, so they passed each other at 11:45 AM.