I know the Pythagorean thereom for the last part. I am not $100\%$ sure with the other parts. Here is the problem:
Marty and Rediat got in a fight. They walked away from each other on seperate paths at a right angle to each other. Marty walks at $2$ km/hr for $20$ minutes, then stops to think. Rediat walks $3$ km/hr for $30$ minutes then he stops to think. Then, suddenly, they both want to apologize and they start running for each other. How far apart are they? How long will it take for them to reach eachother if they run straight at eachother at $5$ km/hr?
What I did is I put 20 minutes over $60$ minutes to get the fraction of $1/3$ for Marty. Then I multiplied that times $2$ (because $2$ km/hr) and got $(1/3 * 2 = 2/3)$km.
For Rediat, $30$ minutes over $60$ minutes, for fraction of $1/2$ for Rediat. Then, I multiplied that times $3$ (for $3$ km/hr) and got $(1/2 * 3 = 3/2)$km.
Then, since it is a right triangle, I did $a^2 + b^2 = c^2$.
$(\frac{2}{3})^2 + (\frac{3}{2})^2= c^2. $
So, $\frac{4}{9} + \frac{9}{4} = c^2$.
$\frac{97}{36}=c^2. $
Is this right? If so, how do I complete the problem (including the $5$ km/hr part). If not, how do I do it correct?
Looks OK to me.
Get $c$ from your value for $c^2$. Don't worry if there is a $\sqrt{}$ - just leave it.
Since their combined speeds are 5 km/hr, use distance = rate*time to get the time from the distance ($c$) and rate that you know.
If they each go 5 km/hr, together they move 10 km/hr, so the rate is twice as much as in the previous paragraph, and the time is, therefore, half of that result.