Find expression for their distance apart after t hours.

[problemsets]

John leaves an intersection at 12noon and heads South at 24 miles per hour, while Jane leaves the intersection at the same time and heads East at 32 miles per hour. Find an expression d for their distance apart (in miles) after t hours.

[Pammy06]

since they are leaving each other perpendicularly, you need to use a right triangle.
The lapse of time is equal so, t is the same for both directions. a=24t for one leg of your triangle and b=32t for the other. c=d is the hyponenuse.
Replace a²+b²=c²(pathagoreum theorem) with the given info above.
(24t)² + (32t)² = d²
solve for d by taking the square root of both sides.
d = sqrt((24t)² + (32t)²)

hope this helps!