Jack the Jaguar can run for only 1.0 min at 13.0m/s before he has to stop to rest, while Zeke the zebra can gallop at 7.25m/s for 5.0 min. How long does Zeke actually have to run for to elude Jack? Can Jack catch Zeke for lunch if they are initially 350m apart?
The first question makes little sense, but the second can be answered by solving
13s = 7.25s+350
s = 60.87
Since Jack has to stop after only 60 seconds, he'll watch Zeke's heels as he escapes. One more second and he'd have had zebra for lunch.
To determine how long Zeke has to run to elude Jack, we need to compare their distances traveled over time and see if Zeke can maintain a lead.
First, let's calculate how far Jack can run in 1.0 minute at a speed of 13.0 m/s. This can be done by multiplying the speed by the time:
Distance Jack can run = Speed * Time = (13.0 m/s) * (1.0 min * 60 s/min) = 780 meters
So Jack can cover 780 meters in 1 minute.
Now, let's calculate how far Zeke can run in 5.0 minutes at a speed of 7.25 m/s:
Distance Zeke can run = Speed * Time = (7.25 m/s) * (5.0 min * 60 s/min) = 2175 meters
So Zeke can cover 2175 meters in 5 minutes.
Since they are initially 350 meters apart, Zeke would need to run for an additional distance of 350 meters to fully elude Jack. This can be determined by subtracting the initial distance from the total distance Zeke can cover:
Additional distance Zeke needs to run = Distance Zeke can run - Initial distance = 2175 meters - 350 meters = 1825 meters
Now, let's calculate the time it would take for Zeke to cover this additional distance at a speed of 7.25 m/s. We can rearrange the equation for speed to solve for time:
Time = Distance / Speed = 1825 meters / 7.25 m/s = 251.72 seconds
Therefore, Zeke would need to run for approximately 251.72 seconds, or about 4 minutes and 12.72 seconds, to completely elude Jack.
As for whether Jack can catch Zeke for lunch if they are initially 350 meters apart, we can compare their distances traveled. Jack can run 780 meters in 1 minute, while Zeke can run 2175 meters in 5 minutes.
If Zeke is able to maintain a lead of 1825 meters (the additional distance he needs to run), Jack will not be able to catch him since Zeke covers a greater distance in the same amount of time. Therefore, if Zeke maintains his speed, he will successfully evade Jack for lunch.