oh man....took some time to solve it...did it in a very long way...
time the train would have done if no accident happened D/x
time when accident happened 60km away:
60/x + 6*(D-60)/5x
now, the difference is 1h12m or 6/5 hours
60/x + 6*(D-60)/5x - D/x = 6/5
rewrite everything as:
(300+6D-360-5D)/5x = 6/5
or (D-60)/5x = 6/5
cross multiply:
30x = 5D-300
now, if the accident happened 120km away:
time traveled before accident 120/x
time after accident:
6*(D-120)/5x
total time: 120/x + 6*(D-120)/5x
now, in this case, the train arrived 1 hour late:
120/x + 6*(D-120)/5x - D/x = 1
rewrite everything:
(120*5 +6D-720-5D)/5x = 1
or
D-120/5x = 1
or 5x=D-120
ok, now we have two formulas:
30x = 5D-300
and 5x=D-120
multiply the second one by 6
30x=6D-720
substitute 30x in the first equation with 6D-720
6D-720 = 5D-300
D = 420
ok, looks good.
5x=D-120
5x = 420-120
5x = 300
x = 60
A
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