On a softball field one person walks from home plate to 3rd

On a softball field, one person walks from home plate to 3rd base at 6\' per sec. and one person jogs from home plate to 1st base at 10\' per sec. How many seconds will it take them to be 270\' apart?

Solution

The softball diamond is a square. There\'s a 90 degree angle between home and first and home and third. When you draw a straight line between the two walkers/joggers, this straight line forms the hypotneuse of the right triangle.
What we want to know is how many seconds will have elapsed until this hypotneuse is 270\' long.
Let t=time that elapses (seconds) until the persons are 270\' apart:
Distance walker travels=6t-------one leg of the right triangle
Distance jogger travels=10t-------other leg of the right triangle
Now we know that (6t)^2+(10t)^2=(270)^2 or
36t^2 +100t^2=72,900 divide each term by 4
9t^2 +25t^2=18225 collect like terms
34t^2=18225 divide each side by 34
t^2=536.03 take sqrt of both sides
t=23.152 sec
CK
6*23.152=138.9 ft
10*23.152=231.52 ft
(138.9)^2+(231.52)^2=(270)^2
19293.21 + 53601.51=72,900
~~~~~~72,900=72,900