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!)
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