SOLUTION: two trains travel toward each other from city a and city b, which are 400 miles apart, and they are traveling at the rates of 110 mph and 90 mph. they started at the same time and

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Question 462486: two trains travel toward each other from city a and city b, which are 400 miles apart, and they are traveling at the rates of 110 mph and 90 mph. they started at the same time and reach city c at the same time.
a)in how many hours the trains will reach to city c between city a and city b?
b) what distance did the faster train travel to reach to city c?
Found 2 solutions by josmiceli, rwm:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d%5B1%5D+ = distance faster train travels
Let +d%5B2%5D+ = distance slower train travels
given:
+d%5B1%5D+%2B+d%5B2%5D+=+400+
faster train:
(1) +d%5B1%5D+=+110t+
slower train:
(2) +d%5B2%5D+=+90t+
----------------
(a)
Add (1) and (2)
+d%5B1%5D+%2B+d%5B2%5D+=+110t+%2B+90t+
+400+=+200t+
+t+=+2+ hrs
They will reach city c in 2 hours
(b)
(1) +d%5B1%5D+=+110t+
(1) +d%5B1%5D+=+110%2A2+
(1) +d%5B1%5D+=+220+ mi
The faster train will travel 220 mi
check:
(2) +d%5B2%5D+=+90t+
(2) +d%5B2%5D+=+90%2A2+
(2) +d%5B2%5D+=+180+ mi
+220+%2B+180+=+400+ mi
OK

Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
110t+90t=400
200t=400
t=2 hours
city a (faster )is 220 miles from c and city b is 180 miles from city c