SOLUTION: A goods train leaves a station at 6 p.m. followed by an express train which leaves at 8 p.m and travels 20 km/ hr faster than good train. The express train arrives at a station 104

Question 959193: A goods train leaves a station at 6 p.m. followed by an express train which leaves at 8 p.m and travels 20 km/ hr faster than good train. The express train arrives at a station 1040 km away, 36 min before the goods train. Find their speeds.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the speed of the goods train in km/hr
= the speed of the express train in km/hr
--------------------
From 6 pm to 8 pm, the goods train gets a
head start of:
km
--------------------
Start a stopwatch when the express train leaves
Let = the time on the stopwatch when the
express train arrives at station.
= time on stopwatch when goods train arrives
--------------------
Equation for the goods train:
(1)
Equation for express train:
(2)
---------------------------------
(1)
(1)
(1)
and
(2)
-----------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
use quadratic formula

and
(2)
(2)
(2)
(2)

------------------------
The speed of the goods train is 80 km/hr
The speed of the express train is 100 km/hr
check:
(1)
(1)
(1)
(1)
OK

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