SOLUTION: Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18 mph, and the other travels due east at a speed of 24 mph. How long until the distan

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Question 1019744: Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18 mph, and the other travels due east at a speed of 24 mph. How long until the distance between them is 90 miles?
I think it's 2 hours something but cannot figure out the mathematical equation to figure it out. Thank you
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18 mph, and the other travels due east at a speed of 24 mph. How long until the distance between them is 90 miles?
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It's a right triangle, and the distance between is the hypotenuse.
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(18t)^2 + (24t)^2 = 90^2
900t^2 = 8100
t = 3 hours

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time of travel for both
+d%5B1%5D+=+18t+
+d%5B2%5D+=+24t+
Their paths form a right triangle and
the distance between them is the
hypotenuse.
Let +d%5B3%5D+ = the distance between them
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+d%5B3%5D%5E2+=+d%5B1%5D%5E2+%2B+d%5B2%5D%5E2+
+d%5B3%5D%5E2+=+%28+18t+%29%5E2+%2B+%28+24t+%29%5E2+
+d%5B3%5D+=+sqrt%28+324t%5E2+%2B+576t%5E2+%29+
+d%5B3%5D+=+sqrt%28+900+%29%2At+
+90+=+30t+
+t+=+3+
In 3 hrs the distance between them will be 90 mi