Question #fe8f6

1 Answer
Feb 12, 2018

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.