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# runners

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Two joggers are running around an oval track in opposite directions. One jogger runs around the
track in 56 seconds. They meet every 20 seconds. How many seconds does it take the second jogger
to run around the track?

Oct 24, 2022

#1
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Oct 24, 2022
#2
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Let the time taken by the 2nd jogger = T

1/56  +  1/T =1/20

1/T =1 / 20  -  1/56

T = 31 + 1/9 seconds - time taken by the 2nd jogger.

Oct 24, 2022
#3
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Two joggers are running around an oval track in opposite directions. One jogger runs around the
track in 56 seconds. They meet every 20 seconds. How many seconds does it take the second jogger
to run around the track?

Place both joggers at the same spot on the track, and fire the starting pistol.

At the rate of 56 seconds to go all the way around, Jogger A runs 1/56 of the track in one second.

So when the two meet, 20 seconds later, Jogger A has run 20/56 of the way around the oval track.

To get there at at the same time, Jogger B had to run 36/56 of the way around in the other direction.

Since it takes Jogger B 20 seconds to run 36/56 of the way around, his speed is (36/56 oval) / (20 sec)

Doing the arithmetic, Jogger B's speed is 36/1120 oval per second.  This is very close to 1/31.1 oval per second.

At 1/31.1 oval per second, it takes Jogger B  31.1 seconds  to run all the way around the oval track.

.

Oct 24, 2022