SOLUTION: A northbound train left at midnight. Three hours later, a southbound train left the same station. At 6 a.m. the two trains were 330 miles apart. Find the rate of each train if

Question 1080922: A northbound train left at midnight. Three hours later, a southbound train left the same station.
At 6 a.m. the two trains were 330 miles apart. Find the rate of each train if the northbound train traveled 10 miles per hour faster than the southbound train.
Draw graph to display problem.
Found 3 solutions by Fombitz, josmiceli, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Let A be the northbound train, B the southbound.
1.
The distance covered by A was,

The distance covered by A was,

The distance between them is,

Substituting from 1,

Solve for .
Then use either equation to solve for .
.
.
.
Is the graph displaying distance traveled versus time?
If so then, between and ,

Then ,

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed of the southbound train
= the speed of the northbound train
-----------------------------------------------
What is the northbound station's headstart in miles
when the southbound train leaves station?

------------------------------------------------
Start a stopwatch when the southbound train leaves station
and time both of the trains
Let = distance southbound train travels
from 3 AM to 6 AM
is the distance northbound train
travels from 3 AM to 6 AM
------------------------------------------------------
Equation for the southbound train:
(1)
Equation for the northbound train:
(2)
---------------------------------------------
(2)
(2)
Plug (1) into (2)
(2)
(2)
(2)
and

--------------------
The speed of the southbound train is 30 mi/hr
The speed of the northbound train is 40 mi/hr
------------------------------------------
check:
(1)
(1)
(1) mi
and
(2)
(2)
(2)
(2)
(2) mi
OK
-------------------------
Hope I got it. Check the math & get a 2nd
opinion if needed

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
A northbound train left at midnight. Three hours later, a southbound train left the same station.
At 6 a.m. the two trains were 330 miles apart. Find the rate of each train if the northbound train traveled 10 miles per hour faster than the southbound train.
Draw graph to display problem.

Let the speed of the northbound train, be S
Then the speed of the southbound train = S - 10
Six (6) hours (midnight - 6:00 a.m.) after leaving, the northbound train covered a distance of 6S miles
Three (3) hours (3:00 a.m. - 6:00 a.m.) after leaving, the southbound train covered a distance of 3(S - 10), or 3S - 30 miles
Since they were 330 mile apart at 6:00 a.m., we get the following DISTANCE equation: 6S + 3S - 30 = 330
9S = 360
S, or speed of northbound train =
Now, subtract 10 from 40 to get the southbound train's speed.
That's it!! Simple enough, right?
Now that the hard part is done, you should be able to graph it. I can't do everything now, can I?
Try it! How else will you learn?
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