A person covered some distance in 12 hours He covered half t

A person covered some distance in 12 hours. He covered half the distance by rail @ 75 km per hour and the rest by car @ 45 km/hr. The total distance covered by him was

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let d=total distance covered
Time spent by rail=(d/2)/75
Time spent by car=(d/2)/45
Now we are told that the above two times add up to 12 hr, so:
(d/2)/75 + (d/2)/45=12 simplify
d/150 +d/90 = 12 or multiply each term by 450 (LCM)
3d+5d=5400
8d=5400
d=675 mi-------------------total distance covered
CK
Time spent by rail=(675/150)=4.5 hr
Time spent by car=(675)/90=7.5 hr
7.5 +4.5=12
12=12