Question 317026: At 5pm, Jill leaves New York City and travels toward Boston at an average rate of 56 miles per hour. At 6pm, Billy leaves Boston and travels toward New York, on the same road as Jill, at an average rate of 50 miles per hour. If they were initially 215 miles apart, at what time do Billy an Jill pass each other?
Remarks: I know we are trying to solve for 't' here, but I'm not sure how to setup the problem. Should Jill be setup as (t+1) or Billy should?? Thanks for your help.
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At 5pm, Jill leaves New York City and travels toward Boston at an average rate of 56 miles per hour. At 6pm, Billy leaves Boston and travels toward New York, on the same road as Jill, at an average rate of 50 miles per hour. If they were initially 215 miles apart, at what time do Billy an Jill pass each other?
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Jill DATA:
rate = 56 mph ; time x hrs ; distance = 56x miles
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Billy DATA:
rate = 60 mph ; time = x-1 hrs ; distance = 60x-60 miles
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Equation:
distance + distance = 215 miles
56x + 60x-60 = 215
116x = 275
x = 2.37 hrs = 2 hrs and 22 minutes
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Time of passing: 5pm = 2 hrs 22 minutes = 7:22 PM
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Cheers,
Stan H.
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Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! At 5pm, Jill leaves New York City and travels toward Boston at an average rate of 56 miles per hour. At 6pm, Billy leaves Boston and travels toward New York, on the same road as Jill, at an average rate of 50 miles per hour. If they were initially 215 miles apart, at what time do Billy an Jill pass each other?
Jill 5.00 pm new york 56 mph
before Billy leaves Boston Jill has traveled 56 miles. He has reached point A
..
Billy's speed = 50 mph.
let them meet at a distance of x miles from Boston
..
Billy will travel distance x
speed = 50 mph
time taken = x/50 hours.
..
In the same time Jill has traveled 215-x-56
Jill has traveled 159-x miles
speed = 56 mph
time = 159-x/56 hours.
x/50 = 159-x / 56
56x=50(159-x)
56x=7950-50x
106x=7950
x=75 distance traveled by Billy
His speed was 56 mph
he took 75/56 hours
= 1.34 hours
at 7.20 pm
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