SOLUTION: It takes Jordan 74 seconds to run around a 416-yard track. How long does it take Arnold to run around the same track if he and Jordan meet in 32 seconds after they start together i

Question 1146363: It takes Jordan 74 seconds to run around a 416-yard track. How long does it take Arnold to run around the same track if he and Jordan meet in 32 seconds after they start together in a race around the track in opposite directions?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance
jordan can run around the 416 yard track in 72 seconds.
formula for jordan becomes rate * 74 = 416
the rate for jordan is 416 / 74 = 5.621621622 yards per second.

arnold runs around the same track in the opposite direction.
they meet after 32 seconds.
in 32 seconds, jordan has run 5.621621622 yards per second * 32 = 179.8918919 yards.
that means that arnold must have run 416 - 179.8918919 = 236.1081081 yards in the same 32 seconds.
rate * time = distance
formula for arnold becomes rate * 32 = 236. 1081081 yards.
the rate for arnold is 236.1081081 / 32 = 7.378378378 yards per second.

at that rate, the formula for arnold to run around the whole track by himself becomes 7.378378378 * time = 416
the time it takes is therefore 416 / 7.378378378 = 56.38095238 seconds.

to verify the rates are ok, then determine the yards that each has traveled in 32 seconds.

for jordan, 5.621621622 * 32 = 179.8918919 yards.
for arnold, 7.378378378 * 32 = 236.1081081 yards.
total yards for both in 32 seconds = 416 yards.

rates look good.

your solution is that it would takes arnold 56.38095238 seconds to run around the same 416 yard track.

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