Jim and Joe were running together. Jim's average speed was 400 meters per minute.Jim started running four minutes before Joe.
ten minutes after Joe started, he caught up with Jim. What was Joe's average speed?
Jim ran for 4 minutes at 400m/min.
his distance when Joe started was thus 1600m
Joe and Jim then both ran for 10 minutes, and Joe ended up running the same distance as Jim, who had run an extra 4000m.
If Joe's speed is x m/min, then
1600 + 4000 = 10x
560 = x
So, Jim ran 1600 + 4000 m = 5600 m
Joe ran 560m/min * 10 min = 5600 m
To find Joe's average speed, we can use the concept of relative speed.
Let's break down the problem step by step:
1. Jim started running four minutes before Joe, implying that Jim had a head start of 4 minutes.
2. In those first four minutes, Jim covered a distance equal to his average speed multiplied by the time taken:
Distance covered by Jim = Jim's average speed * Time taken by Jim = 400 meters/minute * 4 minutes = 1600 meters.
3. After the 4-minute head start, both Jim and Joe were running simultaneously. They covered the same distance from that point.
4. After ten minutes from the time Joe started running, we know that Jim and Joe will have covered the same total distance. Therefore, we can equate their distances covered:
Distance covered by Jim = Distance covered by Joe.
Distance covered by Jim = Jim's average speed * Time taken by Jim (as we already calculated) = 1600 meters.
Distance covered by Joe = Joe's average speed * Time taken by Joe.
5. Since both Jim and Joe covered the same distance after 10 minutes, we can set up the equation:
Jim's distance = Joe's distance.
1600 meters = Joe's average speed * 10 minutes.
6. We can rearrange the equation to find Joe's average speed:
Joe's average speed = Jim's distance / Time taken by Joe = 1600 meters / 10 minutes.
Now, let's calculate the value:
Joe's average speed = 1600 meters / 10 minutes = 160 meters/minute.
Therefore, Joe's average speed is 160 meters per minute.