SOLUTION: Train A travels 20mi/h slower than Train B. It takes Train A 30 minutes longer than Train B to travel 200 miles. How long does it take Train A to make the 200 mile trip? How long d

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Question 411735: Train A travels 20mi/h slower than Train B. It takes Train A 30 minutes longer than Train B to travel 200 miles. How long does it take Train A to make the 200 mile trip? How long does it take Train B to travel 525 miles?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let v = velocity of train A
v+%2B+20 = velocity of train B
Let t = time for train A
t+-+.5 = time for train B
d%5BA%5D+=+d%5BB%5D
write 2 equations: 1 for train A, 1 for train B
A:
200+=+v%2At
B:
200+=+%28v+%2B+20%29%2A%28t+-+.5%29
---------------------
200+=+%28v+%2B+20%29%2A%28t+-+.5%29
200+=+vt+%2B+20t+-+.5v+-+10
By substitution:
200+=+200+%2B+20t+-+.5v+-+10
.5v+=+20t+-+10
v+=+40t+-+20
By substitution:
200%2Ft+=+40t+-+20
200+=+40t%5E2+-+20t
2t%5E2+-+t+-+10+=+0
Use quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+-1
c+=+-10
t+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A%28-10%29+%29%29%2F%282%2A2%29+
t+=+%28+1+%2B-+sqrt%28+1+%2B+80+%29%29%2F4+
t+=+%28+1+%2B+9%29%2F4+ (can't use the negative root)
t+=+5%2F2
It takes train A 2.5 hours to go 200 mi
and
200+=+v%2At
v+=+200%2F2.5
v+=+80
For train B:
200+=+%28v+%2B+20%29%2A%28t+-+.5%29
525+=+%2880+%2B+20%29%2At%5BB%5D
t%5BB%5D+=+525%2F100%7D%7D%0D%0A%7B%7B%7Bt%5BB%5D+=+5.25 hrs
It takes train B 5.25 hrs to go 525 mi