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
