Problem number 21. Ahmad and Jaleh start moving from point A with the same speed in the directions shown. Ahmad walks around the square-shaped garden, right here, and Jaleh walks around the rectangular-shaped one, here. They meet again at A. What is the smallest number of laps around the square-shaped garden that Ahmad can make to meet Jaleh there? One, two, three, four, or five. Ahmad and Jaleh are both moving at the same speed, so they will have to complete the same distance, or the same number of meters, by the time they meet back at A. However, their gardens and the paths around them have different parameters. Ahmad's garden, the square one, has a perimeter of 5 plus 5 plus 5 plus 5, or 20 meters. Jaleh's garden has a perimeter of 10 plus 5 plus 10 plus 5, or 30 meters. Now, since the perimeters are different, the first time that Ahmad comes back to point A, Jaleh will not have gone all the way around her garden. What we need to find here is the least common multiple of 20 and 30. That will give us a distance that each of these people needs to walk around their garden and both end up at the same point. The easiest way here to find the least common multiple is to list the first few multiples of each number. For 20, the multiples are 20 times 1, which is 20, 20 times 2, 40, 20 times 3, 60, 20 times 4, 80, 20 times 5, 100, and hopefully that will be enough. For 30, the multiples are 1 times 30, or 30, 2 times 30, 60, 3 times 30 is 90, and we could keep going, but we actually already found our least common multiple. The number that occurs in both lists is 60. So 60 is the smallest number that is a multiple of both 20 and 30, and it's the distance that Ahmad will walk around his garden and Jaleh will walk around her garden by the time they meet at point A again. The question in the problem is, what is the smallest number of laps around the square-shaped garden that Ahmad can make to meet Jaleh there? We found the distance, which is 60 meters, and we just need to find the number of laps. If Ahmad walks 60 meters and the garden is 20 meters around, we just need to divide 60 meters by 20 meters to get that he will make three laps around the garden when he meets Jaleh. So the answer is C, 3.

Ahmad

Jaleh

square garden

rectangular garden

least common multiple