Two soccer players start at opposite sides of an 80-m field. One runs at 4 m/s and the other runs at 5 m/s. If they run back and forth for 15 mins, how many times will they pass each other?
**The answer is 25 but I keep getting 45!!
To solve this problem, let's break it down step by step:
Step 1: Convert the given time from minutes to seconds.
15 minutes = 15 x 60 = 900 seconds.
Step 2: Find the total distance covered by each player in 900 seconds.
Player 1:
Distance = speed x time
Distance = 4 m/s x 900 s = 3600 m
Player 2:
Distance = speed x time
Distance = 5 m/s x 900 s = 4500 m
Step 3: Find the total number of times the players pass each other.
To calculate this, divide the total distance covered by both players by the length of the field.
Total distance covered by both players = Distance covered by Player 1 + Distance covered by Player 2
Total distance covered by both players = 3600 m + 4500 m = 8100 m
Number of passes = Total distance covered by both players / Length of the field
Number of passes = 8100 m / 80 m = 101.25
Since the players pass each other at each end of the field, we need to round to the nearest whole number. Therefore, the players will pass each other approximately 101 times.
However, it is important to note that this is only an approximation, and the exact number of passes may vary slightly.
To solve this problem, we need to calculate the distance each player will cover in 15 minutes and then determine how many times they will pass each other. Let's break down the problem step by step:
1. Convert 15 minutes to seconds, as the players' speeds are given in meters per second. There are 60 seconds in a minute, so 15 minutes is 15 * 60 = 900 seconds.
2. Calculate the distance covered by the faster player in 900 seconds. The faster player runs at a speed of 5 m/s, so the distance covered is speed * time = 5 * 900 = 4500 meters.
3. Similarly, calculate the distance covered by the slower player in 900 seconds. The slower player runs at a speed of 4 m/s, so the distance covered is speed * time = 4 * 900 = 3600 meters.
4. Now, we need to figure out how many times they will pass each other. Since they start on opposite sides of the field, they will meet each other when the sum of their distances covered is equal to the length of the field.
5. The total distance covered by both players in one round trip is the sum of their individual distances. So, the total distance is 4500 + 3600 = 8100 meters.
6. The length of the field is given as 80 meters. To find the number of times they pass each other, we divide the total distance covered by the length of the field: 8100 / 80 = 101.25.
7. Since they pass each other at the start and finish, we need to subtract 2 from the total number of passes: 101.25 - 2 = 99.25.
Here's where the confusion might have occurred. Since we started with 900 seconds (15 minutes) and both players cover the full distance multiple times, the answer obtained is in fractions. However, the question asks for the number of whole passes.
8. To convert the passes back to whole numbers, we need to round down the result. Therefore, the players will pass each other 99 times.
It seems there was an error with the answer you initially mentioned (25). However, the correct answer is 99.