SOLUTION: Hello, I'm having trouble setting up this problem. Answers in the back of the book but I need to understand it!! Thank you! Two cyclists leave from an intersection at the same ti

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Question 840944: Hello, I'm having trouble setting up this problem. Answers in the back of the book but I need to understand it!! Thank you!
Two cyclists leave from an intersection at the same time. One travels due north at a speed of 15 miles per hour, and the other travels due east at a speed of 20 miles per hour. How long until the distance between the two cyclists is 75 miles?

Thanks again! Iris
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Distance = Rate * Time
D%5B1%5D=15%2AT
D%5B2%5D=20%2AT
Since one is going north and the other is going east, their distances are legs of a right triangle and the distance between them is the hypotenuse of the right triangle. Use the Pythagorean theorem.
D%5E2=D%5B1%5D%5E2%2BD%5B2%5D%5E2
D%5E2=%2815T%29%5E2%2B%2820T%29%5E2=75%5E2
225T%5E2%2B400T%5E2=5625
Take it from there to solve for T