SOLUTION: A bus leaves a station at 1 PM, traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time
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Question 22284: A bus leaves a station at 1 PM, traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses be 274 miles apart? Found 2 solutions by Paul, JWG:Answer by Paul(988) (Show Source):
You can put this solution on YOUR website! 274(44(t+1))=274(48t)
274(44t+44)=13152t
12056t+12056=13152t
12056t-12056t+12056=13152t-12056
1096t=12056
t=11
1+11=12
hence, at 12 A.M. they will be 274 miles apart.
You can put this solution on YOUR website! Bus 1:
Rate: 44, Time: X+1
Bus 2:
Rate: 48, Time: X
Bus 1 is 'X+1' since it left an hour before Bus 2 whose time traveled is 'x' since we don't know how long it is traveling.
We want to find out when the combined rate and times of the two buses = 274
Rate*Time=Distance
Bus 1's Distance+Bus 2's Distance=274
44(x+1)+48x=274
44x+44+48x=274
92x=230
x=2.5
Don't celebrate and think it took 2.5 hours. We want to know how long it took starting from when the first bus left for the two buses to be 274 miles apart.
Bus 1: Time=(x+1)=(2.5+1)=3.5 hours or 3 hours, 30 minutes.
1pm+3 hours 30 minutes=4:30pm
You can always plug in 2.5 into the original equation to double check.
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