SOLUTION: an engine pulls a train 140 miles. then a second engine, whose average rate is 5 miles per hour faster than the first engine, takes over and pulls the train 200 miles. The total ti

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Question 231501: an engine pulls a train 140 miles. then a second engine, whose average rate is 5 miles per hour faster than the first engine, takes over and pulls the train 200 miles. The total time required for both engines is 9 hours. Find the average rate of each engine.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Write a separate equation for the 2 engines
1st engine:
(1)
2nd engine:
(2)
----------------------
given:
mi
mi
mi/hr
hrs
----------------------
Now I can rewrite the equations
(1)
(1)
and
(2)
(2)
(2)
-----------------------
At this point, I have 2 equations and
2 unknowns, so it's solvable
(2)
(2)
Now I substitute (1) in (2)
(2)
(2)
Now I can substitute r[1] from (1) in (2)
(2)
Multiply both sides by
(2)
(2)
(2)
Solve using quadratic formula

(reject the negative solution)

hrs
and, since

hrs
From (1)
(1)

mi/hr
From (2)

mi/hr
The average rate of the engines is 35 mi/hr and 40 mi/hr
check:
(2)

OK