Tortoise vs. Hare Race: Length of Race Solved

[pelikon]

Can someone help me with this question? I am not sure where to go with it.

A speedy tortoise can run with a velocity of 10 cm/sec and a hare can run 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). What was the length of the race?

thanks

 

[LowlyPion]

Can someone help me with this question? I am not sure where to go with it.

A speedy tortoise can run with a velocity of 10 cm/sec and a hare can run 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). What was the length of the race?

thanks

Welcome to PF.

Maybe write an equation that describes the distance the Hare goes (including the 120 sec pit stop) as a function of time and add the 20 cm he loses by and the distance the Tortoise goes with time and then set the two equations equal?

 

[baba89]

for your help

I can provide an explanation for this scenario. The length of the race can be calculated by using the formula: distance = velocity x time. In this case, the distance traveled by both the tortoise and the hare can be represented as follows:

Distance of tortoise = 10 cm/sec x t (time taken for the race)
Distance of hare = 100 cm/sec x (t - 2) (since the hare stops to rest for 2 minutes)

Since the tortoise wins by a shell, we can set the distances equal to each other and solve for t:

10t = 100(t-2) + 20
10t = 100t - 200 + 20
80t = 180
t = 2.25 minutes

Therefore, the length of the race is 2.25 minutes or 135 seconds. It is important to note that this calculation assumes that both the tortoise and the hare maintain a constant velocity throughout the race.