Joan and Jim run around the same circular track, starting together and running in the same direction....more below?
...Joan takes 3 minutes to complete one circuit of the track while Jim takes 74 minutes
to run the same distance. Joan passes Jim every x minutes. Find the value of x.
It's supposed to be 7 min sorry
- PuzzlingLv 73 weeks agoFavorite Answer
Are you sure about the numbers? There seems to be quite a disparity between Joan's time and Jim's time.
In any case, Joan runs 1/3 of the course every minute. Jim runs 1/74 of the course every minute.
So every minute, Joan increases her distance ahead of Jim by 1/3 - 1/74 of a track length.
1/3 - 1/74
= 74/224 - 3/224
We want to know when Joan will lap Jim by getting exactly 1 lap ahead.
(71/224)x = 1
x = 1 / (71/224)
x = 224/71
x = 3 11/71 minutes
In other words, she'll run a full lap and then about another 9.3 seconds and will catch up with Jim who has barely gone anywhere.
If your numbers are different, just use this formula.
Let A be Joan's time to complete one lap
Let B be Jim's time to complete one lap
x = AB / (B - A)
For example, if Joan takes 3 minutes and Jim takes 7.5 minutes, we would have:
x = (3 * 7.5) / (7.5 - 3)
x = 22.5 / 4.5
x = 45/9
x = 5 minutes
With your numbers, about 3 minutes 9.3 seconds
x = (3 * 7) / (7 - 3)
x = 21/4
x = 5 1/4 minutes
With your revised numbers, 5 minutes 15 seconds
- 3 weeks ago
Let d be the distance of the track
Joan's speed (v) = d/t = d/3
Jim's speed (v) = d/t = d/72
Shouldn't be too hard to solve if you can imagine what's going on