Tommy and Zach are starting out at the same position. Tommy runs north at 5 miles per hour and Zach starts to run east 2 hours later at the rate of 8 miles per hour. How long until Tommy and Zach are 16 miles apart? Round to the nearest tenth if necessary.

Question

Cuddle Pig

Mathematics

16 July, 13:52

Tommy and Zach are starting out at the same position. Tommy runs north at 5 miles per hour and Zach starts to run east 2 hours later at the rate of 8 miles per hour. How long until Tommy and Zach are 16 miles apart? Round to the nearest tenth if necessary.

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Roger Berg · Answer 1

Alright, so that means sqrt (x^2+y^2) is the distance apart using the Pythagorean Theorem, using x=Tommy's distance from the start and y=Zach's distance. Since sqrt (x^2+y^2) = 16, that means that x^2+y^2=256 by squaring both sides. Tommy's length can be used as 5z (z=hours), and Zach's length is 8z-16 (since 16 miles is what he missed by starting 2 hours later). We could then write it as (5z) ^2 + (8z-16) ^2=256, and then by multiplying it out we get

25z^2 + 64z^2-256z + 256=256. Subtracting 256 from both sides, we get

25z^2+64z^2-256z=0 and dividing by z we get 89z-256=0. Adding 256 to both sides, we get 89z=256 and z=256/89 and rounded to 2.9 hours