SOLUTION: a passenger train leaves a train depot 1 hr after a freight train leaves the same depot. the freight train is traveling 15 mph slower than the passenger train. find the rate of eac

Question 1060836: a passenger train leaves a train depot 1 hr after a freight train leaves the same depot. the freight train is traveling 15 mph slower than the passenger train. find the rate of each train if the passenger train over takes the freight train in 3 hrs.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the passenger train in mi/hr
= the speed of the freight train in mi/hr
Let = the distance in miles the passenger train
travels until it overtakes the freight train
-------------------------------------------------
Find the freight train's head start in miles
mi
--------------------------------------------------
Equation for the passenger train:
(1)
Equation for the freight train:
(2)
(2)
(2)
(2)
Substitute (1) into (2)
(2)
(2)
and

---------------------
The passenger's speed is 60 mi/hr
The freight train's speed is 45 mi/hr
------------------------------------
check:
(1)
(1)
(1) mi
and
(2)
(2)
(2)
(2)
(2) mi
OK

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
a passenger train leaves a train depot 1 hr after a freight train leaves the same depot. the freight train is traveling 15 mph slower than the passenger train. find the rate of each train if the passenger train over takes the freight train in 3 hrs.

Let speed of passenger train be S
Then speed of freight train = S - 15
We then get the following DISTANCE equation: 3S = 4(S - 15)
3S = 4S - 60
3S - 4S = - 60
- S = - 60
S, or speed of passenger train =
Speed of freight train:
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