Asked by Livia
Two teams compete in a relay race; they are composed of four members, each of whom runs 100
meters. All the members of team B run at b meters per second (mps). The first three members of
team A can only run 5b/6 mps, while the fourth member runs at a mps. Find a/b if the race is a
tie
meters. All the members of team B run at b meters per second (mps). The first three members of
team A can only run 5b/6 mps, while the fourth member runs at a mps. Find a/b if the race is a
tie
Answers
Answered by
mathhelper
team B
each runs at b m/s , so time for team B = 400/b seconds
team A
time for 3 runners = 300/(5b/6)
time for last runner = 100/a
for a tie, their times are equal
100/a + 300/(5b/6) = 400/b
100/a + 360/b = 400/b
100/a = 40/b
40a = 100b
a/b = 100/40 = 5/2
each runs at b m/s , so time for team B = 400/b seconds
team A
time for 3 runners = 300/(5b/6)
time for last runner = 100/a
for a tie, their times are equal
100/a + 300/(5b/6) = 400/b
100/a + 360/b = 400/b
100/a = 40/b
40a = 100b
a/b = 100/40 = 5/2