<p>a turtoise can run with a speed of 10 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 minutes. the turtoise wins by 20 cm. how long does the race take?</p>
<p>first, calculate the hare’s speed, which is 10 x 20 = 200 cm/s, then you convert the 2 minutes into seconds, which is 120 seconds, and now you set up your equation.
We know that speed x time = distance</p>
<p>We let t be time.
We have (200)(t-120) +20= 10(t)
This is because the hare spent 120 seconds less time running than the tortoise, and lost by 20 cm, so to make an equality, the hare would have to move an extra 20 cm</p>
<p>Now we solve for t
200t - 24000 + 20 = 10t
190t = 23980
t = 126.21 s</p>
<p>You can check this by doing the following:
Subtract 120 s from the time for the amount of time the hare spent running, and we have 6.21 s. Multiply that by the hare’s speed and we have 1242 cm
that the hare traveled</p>
<p>Multiply the time t by the tortoise’s speed to get 1262.1 cm that the tortoise traveled. As you can see the tortoise traveled about 20 cm more than the hare. The difference is not exactly 20 cm due to roundoff error.</p>
<p>fantastic explanation gator</p>
<p>thanks so much</p>