SOLUTION: A diesel train left Miami and traveled toward Johannesburg at an average speed of 10 mph. A freight train left 11 hours later and traveled in the opposite direction with an average

Question 919850: A diesel train left Miami and traveled toward Johannesburg at an average speed of 10 mph. A freight train left 11 hours later and traveled in the opposite direction with an average speed of 60 mph. How long does the freight train need to travel before the trains are 390 mi. apart?
I know that I am supposed to set up a distance, rate, time chart and fill in the information and then set up and equation, but I am not entirely sure how to set up the equation here, because of the fact that the freight train left 11 hours later.
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
r*t+R*T=D
(11+x)*10+60x=390
110+10x+60x=390
70x=280
x=4 hours

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I use a logical story-line approach
What is the diesel train's head start in miles?

mi
-------------------
Start a stopwatch when the freight train leaves Miami
Let = time in hrs on the stop watch when
the trains are mi apart
Let = the distance in miles that the
freight train travels until they are mi apart
----------------------------------------------
Diesel's equation:
(1)
Freight train's equation:
(2)
-----------------------
Substitute (2) into (1)
(1)
(1)
(1)
(1)
---------------
The freight train travels for 4 hrs until they are 390 mi apart
check:
(2)
(2)
and
(1)
(1)
(1)
OK

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