Two joggers are running toward each other. They start off being 5 miles apart. Joe, leaves at 7:00 AM and

Jack leaves at 7:30 AM. If Joe travels at 4 mph and Jack at 5mph, at what time will they pass each other?

Answer: Hello mate!

the initial distance between Joe and Jack is 5 miles.

we know that Joe travels at 4 mph and jack travels at 5mph.

Now, let's define the 7:00 AM as our time zero, where the time is measured in hours.

We know that Joe starts running at t = 0h and Jack starts running at t = 0.5h

then the position equations are J1 for joe and J2 for Jack.

J1 (t) = 4mph*t

J2 (t) = 5mph * (t - 0.5h)

where the - 0.5h appears because Jack starts 0.5h after.

If they run towards each other, then they will met when J1 (t) + J2 (t) = 5mi, wich means that between the two runned the 5 miles that separated them:

J1 (t) + J2 (t) = 4t + 5 (t - 0.5) = 4t + 5t - 2.5 = 9t - 2.5 = 5

and now we want to isolate t

9t - 2.5 = 5

9t = 5 + 2.5 = 7.5

t = 7.5/9 = 0.8333 ... hours

Then they well met 0.83 hours after the 7:00 Am

We also could write this in a more elegant way:

we know that one hour has 60 minutes, then a 0.83333 ... of an hour has 0.83*60 = 50 minutes

Then they met at 7:50 AM

Answer:9.6 mind