Question 1168485: Trains at each end of a 26 km long tunnel start at the same time. Find the speed (in km/hr) of the faster train if it travels 8.1 km/h faster than the other. They pass each other in the tunnel after 12.4 minutes.
Express your answer to three significant digits. Do not include units in your answer.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! slower travels at x km/min (note units) *12.4 min or 12.4x km
faster travels at (x+0.135)km/min and the 0.135 is 8.1 km/h converted to min.and its distance is 12.4(x+0.135)
or 12.4x+1.674 km
Those two describe 26 km in distance since the time is already considered.
12.4x+12.4x+1.674 km=26 km
24.8 x= 24.326 km
x=0.9809 km/min (not rounded from calculator).
multiply by 60 for x=58.85 or 58.9 km/h and x+8.1 =67 km/h, the answer being 58.9, 67, without units.
Check using hours
The two are approaching each other at 2x+8.1 km/h. In 12.4 minutes they meet, or 0.206667 hours.
that is the time for the combined distance to be 26 km, so the combined speed is 26/0.2066667 or 125.80 km/h
x+x+8.1=125.8
2x=117.7
x=58.85 km/h as above.
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