Question 359546
Jim and John drive from point A to point B in separate cars.
 Jim leaves at 6 am and arrives at 4 pm. John leaves at 10 am and arrives at 3 pm.
 Assume both men drive at constant speeds.
 Find when John catches up with Jim.
:
Let d = distance from A to B
Jim's travel time: 10 hrs (6am to 4pm)
Jon's travel time: 5 hrs (10am to 4pm
:
Let t = Jon's travel time when he catches Jim
Then
(t+4) = Jim's travel time when this happens (Jim leave 4 hrs earlier)
and we know
{{{d/10}}} = Jim's speed
and
{{{d/5}}} = Jon's speed
:
When Jon catches Jim, they will have traveled the same distance; Dist = speed * time.
{{{d/10}}}(t+4) = {{{d/5}}}*t
multiply both sides by 10 to get rid of the denominators, results
d(t+4) = 2dt
divide both sides by d
 t + 4  = 2t
4 = 2t - t
t = 4 hrs, Jon's travel time
then
4 + 4 = 8 hrs; Jim's travel time
:
10 am + 4 hrs = 2 pm when Jon overtakes Jim
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