SOLUTION: I need help with a word problem. I would need the formula to do this and the answer. The problem is, there is a train (train A) that is traveling east at 10 mph. There is a trai

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Question 248671: I need help with a word problem. I would need the formula to do this and the answer. The problem is, there is a train (train A) that is traveling east at 10 mph. There is a train (train B)that is traveling west at 8 mph. In the middle there is a boy walking on the tracks he is traveling east at 0.5 mph. Each train is 10 miles from the boy when they start out. Who will hit the boy first. and where in miles.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You actually have two problems here.
You need to find out when train A and the boy meet and when train B and the boy meet.
Train A and the boy will meet after traveling the same amount of time.=time ta
Train B and the boy will meet after traveling the same amount of time.=time tb
or How far train B would have gone in the same time as it took train A to hit the boy.
How about distance?
Well for going east the boy has a 10 mile head start so you have to add 10 miles to his distance.
Going EAST
the boy travels at .5mph for ta time
rate times time =distance
x=mile marker from train a
.5*ta=x-10
.5*ta+10=x
Train A travels at 10mph
rate times time =distance
10*60*ta=x
set them equal
.5*ta*60+10=10*ta*60
multiply both sides by 2
ta+20=2*10*ta
ta+20=20ta
subtract ta from both sides
20=19ta
divide by 19 (both sides)
20/19=ta
1.0526 hours
63.1578 minutes
1/2*1.0526=.5263 miles from the boys start
now train B will have gone 8.4214
1.5786-.5263=1.05226 from the boy after 1.0526 hours
Which will be 1.5786 miles from the boys start and 1.05226 miles from the boy at the same time.
So train A will have hit the boy first
Check for reasonableness
after one hour
train A will have gone 10 miles at 10 mph
train B will have gone 8 miles at 8 mph
The boy will have gone .5 miles at 1/2 mile an hour
We could have also calculate exactly when and where train B and the boy wold have met and compared to train A but since we weren't asked that there was no need to do that.