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Let the speed of train and car be x km/hr and y km/hr respectively .
For train-
Distance travelled=160km
Speed=xkm/hr
Time=distance / speed
= 160/x
For car-
Distance travelled=total distance -distance travelled by train=760-160=600km
Time taken=600/y
Now total time taken=8hrs
160/x+600/y=8
160y+600x=8xy........... (1)
II..CASE
For train-
Distance=240km
Time=240/x
Forcar-
Distance=520km
Time=520/y
Total time=
12min+8hrs
12/60 +8
123/15 hrs
240/x+520/y=123/15
3600y+7800x=123xy........ (2 )
Multiplying eqn (1)by 13,
2080y+7800x=104xy
Subtracting eq (2) from (1)
2080y+7800x=104xy
3600y+7800x=123xy
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(-) (-) (-)
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1520y =19xy..... (7800x gets cancelled)
(Y on both sides gets cancelled)
1520=19x
1520/19=x
X=80km/hr
Substituting in eq (1)
160y+600×80=8×80y
160y+48000=640y
160y-640y=-48000
-480y=-48000
Negative sign gets cancelled
Y=48000/480=100km/hr
Speed of train=x=80km/hr
Speed of car=y=10km/hr