# 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

### 2 Answers

- 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

= 71/224

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

Answer:

With your numbers, about 3 minutes 9.3 seconds

Update:

x = (3 * 7) / (7 - 3)

x = 21/4

x = 5 1/4 minutes

Answer:

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

As I said at the bottom, use the formula and plug in a=3, b=7.