Help: A hare and a tortoise problem

[evomunkie]

A hare and a tortoise compete in a race over a course 5.00 km long. The tortoise crawls straight and steadily at its maximum speed of 0.740 m/s toward the finish line. The hare runs at its maximum speed of 7.00 m/s toward the goal for 0.800 km and then stops to taunt the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.

how do i go about doing this.

 

[cristo]

You need to show some work before we can help you. Do you have no thoughts at all? Have you no equations which may be useful?

 

[m2003]

I would approach this problem by first setting up a mathematical model to represent the situation. The key variables in this problem are the distance, speed, and time of both the hare and the tortoise.

Let's start by defining some variables:
- d: distance between the starting point and the finish line (5.00 km)
- v_t: tortoise's maximum speed (0.740 m/s)
- v_h: hare's maximum speed (7.00 m/s)
- t: time taken by both animals to reach the finish line

Now, we can use the equation d = v*t to calculate the time taken by the tortoise to reach the finish line:
5.00 km = 0.740 m/s * t
t = 5.00 km / 0.740 m/s
t = 6760 seconds

Next, we need to determine the distance the hare covers before stopping to taunt the tortoise. This can be calculated using the same equation:
0.800 km = 7.00 m/s * t_h
t_h = 0.800 km / 7.00 m/s
t_h = 0.114 seconds

Now, let's consider the time taken by the tortoise to crawl the same distance (0.800 km):
0.800 km = 0.740 m/s * t_t
t_t = 0.800 km / 0.740 m/s
t_t = 1081 seconds

This means that the tortoise will take 1081 seconds to reach the point where the hare stopped to taunt. In this time, the hare would have covered a distance of:
d_h = v_h * t_t
d_h = 7.00 m/s * 1081 seconds
d_h = 7567 meters

So, the hare can let the tortoise approach as close as 7567 meters before resuming the race. Any closer, and the tortoise would win in a photo finish.

In conclusion, by using mathematical modeling and equations, we can determine the distance at which the hare can let the tortoise approach before resuming the race, which the tortoise ultimately wins.