SOLUTION: A train leaves Perryville at 6:00 AM and travels east at a rate of 64 mph. As it reaches its destination, Granite City, a westbound train departs from Granite City for Perryville,

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Question 350071: A train leaves Perryville at 6:00 AM and travels east at a rate of 64 mph. As it reaches its destination, Granite City, a westbound train departs from Granite City for Perryville, traveling at a rate of 48 mph. How far is it from Perryville to Granite City by train if the westbound train gets to Perryville at 9:30 AM?
I tried making a chart and I know that one has to complete its trip before the other begins thus making two entire trips. Train 1 travels at 64 mph and Train 2 travels at 48 mph and they both complete the distance in 210 minutes. Distance=Rate*Time so the problem is essentially two problems with their answers added together (correct?) but the issue is what to use in the time box of my chart. Distance is blank and is RT with RT containing a variable. How do I find out what goes in the time box? how do I find the distance traveled by both trains and the time it took each train to complete the trip?
Thanks so much!!! :)
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Speed to granite city = 64 mph
speed to Perryville = 48 mph.
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The ratio of their speeds = 64/48 = 4/3
While going to grainte city if the time is t
the time to go to perryville itwill take more time = 4t/3 hours.
Both the times when added = 3 1/2 hours =7/2 hours
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t+ (4t/3) = 7/2
(3t+4t) /3 = 7/2
7t/3= 7/2
7t= 3*7/2
t= 3/2 hours
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time taken to go to granite city = 3/2 hours
speed = 64 mph
distance = 64*3/2
distance = 32*3= 96 miles
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Time to go to Perryville = 4t/3 = 4/3*3/2=2 hours
speed = 48 mph
distance = 48 * 2 = 96 miles