Question

a turtle and a snail are 360 meters apart, and they start to move toward each other at 3 pm. if the turtle is 11 times as fast as the snail, and they meet at 3:40 p.m, find the speed of each.

Answer 1

Speed= distance/ time
speed = 360 / 40 = 90

Answer 2

Let u be speed of snail and x be distance traveled by snail.

We have been given that turtle is 11 times as fast as snail. So speed of turtle will be $11\cdot u$. We are also given that they traveled a distance of 360 kilometers. So distance traveled by turtle will be $360-x$.

Furthermore, we are given that they took 40 minutes to complete total distance.

Since we know $\text{Speed}=\frac{\text{Distance}}{Time}$

After substituting our given information into this formula we will get two equation and two unknowns.

$u=\frac{x\text{ metres}}{40\cdot 60\text{ seconds}}$

$11\cdot u=\frac{(360-x)\text{ metres}}{40\cdot 60\text{ seconds}}$

Now substituting u's values in second equation we will get

$11\cdot \frac{x\text{ metres}}{240\text{ seconds}}=\frac{(360-x)\text{ metres}}{240\text{ seconds}}$

$11\cdot x =360-x\\ 12\cdot x=360\\ x=30\text{ metres}$

Now we will find speed of snail (u),

$u=\frac{30\text{ metres}}{240\text{ seconds}}\\ u=\frac{1\text{ metres}}{8\text{ seconds}}$

Now let us find speed of turtle (11u),

$11\cdot u=11\cdot \frac{1\text{ metres}}{8\text{ seconds}}\\ \\ =\frac{11\cdot \text{ metres}}{8\text{ seconds}}$

Therefore, speed of snail is 1/8 meters per second and speed of turtle is 11/8 meters per second.