Question

A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 cm. How long does the race take?

Answer 1

Answer: The race takes 126.21 seconds.

Explanation:

By definition:

$d=Vt$

Where "V" is speed, "d" is distance and "t" is time.

We know that the tortoise can run with a speed of $10\ \frac{cm}{s}$, then:

$V_{tortoise}=10\ \frac{cm}{s}$

Since the hare can run exactly 20 times as fast, its speed is:

$V_{hare}=20(10\ \frac{cm}{s})=200\ \frac{cm}{s}$

Let be "x" the distance in centimeters traveled by the hare.

We know that the tortoise  tortoise wins by 20.0 centimeters, then:

$d_{tortoise}=x+20$

Let be "t" the time in seconds the race takes.

Since the hare stops to rest for 2.00 minutes (or 120 seconds), the time it takes to travel is given by:

$t-120$

 

Then, we can write the following expression for the tortoise:

$x+20=10t$     [Equation 1]

And this expression for the hare:

$x=(200)(t-120)$

$x=200t-24,000$    [Equation 2]

Now we must substitute [Equation 2] into [Equation 1] and solve for "t":

$(200t-24,000)+20=10t\\\\190t=23,980\\\\t=126.21$

The race takes 126.21 seconds.