SOLUTION: Jon leaves for chicago at 3:30. At 5:00 Karl leaves from the same place and heads for Chicago. If Jon averages 50 miles per hour and Karl averages 62 miles per hour, what time does

Question 103091: Jon leaves for chicago at 3:30. At 5:00 Karl leaves from the same place and heads for Chicago. If Jon averages 50 miles per hour and Karl averages 62 miles per hour, what time does Karl overtake Jon?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Most problems like this one require you to figure out "what's equal." In this case, the distance traveled is equal when Karl catches up with Jon. Since Karl left 1.5 hours after Jon, his travel time will be less than Jon's; so let's call it t. That means John's travel time will be t+1.5. We know Karl's average speed is 62, and Jon's is 50. Now, we turn our attention to the standard distance formula: d = r*t.
djon = 50*(t+1.5)
dkarl = 62(t)
When Karl catches Jon, dkarl = djon.
Substituting, we have:
50*(t+1.5)=62t
Multiplying through on the left:
50t+75=62t
Subtracting 50t from both sides:
75 = 12t
t = 75/12 = 6.25 hr, which is how long Karl drove.
We know that Jon's travel time is t+1.5, so he will have travedl 7.75 hr.
Checking:
62*6.25=387.5
50*7.75=387.5
So that checks.
But, always look back at what the question asks!
It asks "at what time does Karl overtake Jon?"
Well, Karl left at 5:00 and drove for 6.25 hr to catch Jon. So the time when he overtakes Jon will be 11:15 (Note that .25 of an hour is 15 minutes, so you show it in time format 11:15, not decimal 11.25!)
RELATED QUESTIONS
Mr.Black leaves Chicago at 8:00 a.m. and drives north on the highway at an average speed... (answered by checkley77)

There are two trains. One train leaves at 5:00 PM From Chicago and is traveling at 50... (answered by jorel1380)

At 9 am a freight train starts from L.A. and heads for Chicago at 50 mph. 2 hours later,... (answered by Paul)

At 1:00 p.m. a car leaves St. Louis for Chicago, traveling at a constant speed of 65... (answered by ankor@dixie-net.com)

A plane leaves Chicago headed for Los Angeles at 540 mph. One hour later, a second plane (answered by checkley75)

paul leaves chicago and travels east at 50 mph. aaron leaves detroit at the same time... (answered by lwsshak3)

I need help setting up this distance word problem. Chicago and Green Bay are about 200 (answered by lwsshak3)

if a train leaves detroit at 10 pm(est)headed west toward chicago at 70 miles per hour... (answered by Greenfinch)