SOLUTION: A goods train leaves a station at 6p.m.,followed by an express train which leaves at 8p.m. and travels 20km per hr faster than the goods train. The express train arrives at a stati
Question 1084833: A goods train leaves a station at 6p.m.,followed by an express train which leaves at 8p.m. and travels 20km per hr faster than the goods train. The express train arrives at a station,1040 km away, 36 min before the goods train. Assuming that the speeds of both the trains remain constant between the two stations;calculate their speeds. I have this question. please solve this. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A goods train leaves a station at 6p.m.,followed by an express train which leaves at 8p.m. and travels 20km per hr faster than the goods train.
The express train arrives at a station, 1040 km away, 36 min before the goods train.
Assuming that the speeds of both the trains remain constant between the two stations;calculate their speeds.
:
let s = the speed of the goods train
the express is 20 km/h faster, therefore:
(s+20) = the speed of the express
:
Change 36 min to hrs; 36/60 = .6 hrs
From the information given we know that the Goods train travel time was 2.6hr more the express.
:
Write time equation; time = dist/speed
Goods time - express time = 2.6 hrs - = 2.6
multiply equation by s(s+2)
s(s+20)* - s(s+20)* = 2.6s(s+20)
Cancel the denominators
1040(s+20) - 1040s = 2.6s^2 + 52s
1040s + 20800 - 1040s = 2.6s^2 + 52s
a quadratic equation
2.6s^2 + 52s - 20800
simplify, divide by 2.6
s^2 + 20s - 8000 = 0
you can use the quadratic formula but this will factor to
(s+100)(s-80) = 0
s = 80 km/h is the speed of the Goods train
and obviously
100 km/hr is the speed of the Express
:
:
You can confirm this, find the time for each and see the difference
