Speed and Races
Praveena and Saveena ride their bicycles along a path that parallels two side-by-side train tracks running the east/west direction. Praveena rides east at 20 miles per hour, and Saveena rides west at 20 miles per hour. Two trains of equal length, traveling in opposite directions at constant but different speeds each pass the two riders. Each train takes exactly 1 minute to go past Praveena. The westbound train takes 10 times as long as the eastbound train to go past Saveena. The length of each train is (m/n) where m and n are relatively prime positive integers. Find m+n.
The answer is 49.
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1 solution
x= length of train for both trains For Praveena, the time it takes to overtake her: x/(20+z)=1/60 for westbound train at speed z. (eq1) x/(y-20)=1/60 for eastbound rain at speed y. (eq2) For Saveena, the times it takes to overtake her: x/(z-20)=10t/60 for westbound train at speed z ( eq3) x/(y+20)=t/60 for eastbound train to overtake her at speed y ( eq4) Solve for x. t=11/20 seconds, x=22/27 miles, y=620/9 mph, z=260/9 mph