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A bus leaves a station at 1 pm traveling west at an average rate of 44 miles per hour. One hour later a second bus leaves the same station, traveling east at an rate of 48 miles per hour. At what time will the two buses be 274 miles apart?
Let t = travel time of the westbound bus when they are 274 mi apart
(t-1) = travel time of the eastbound bus when they are 274 mi apart
Write a distance equation: Distance = speed * time
West bus dist + East bus dist = 274 mi
44t + 48(t-1) = 274
44t + 48t - 48 = 274
92t = 274 + 48
92t = 322
t = 322/92
t = 3.5 hrs is the travel time of the west bound bus
Then we know:
2.5 hrs is the travel time of the east bound bus
Find the time:
1:00 + 3:30 = 4:30 PM, time they will be 274 mi apart
Check solution by finding the sum of the distances:
44(3.5) + 48(2.5) =
154 + 120 = 274 mi as given
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