Two boats leave the same dock

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Two boats leave the same dock at the same time, one travelling due west at 9 miles per hour and the other due north at 15 miles per hour. How many miles apart are the boats after three hours?

Solution: To get the answer of this question , it would be better to sketch it first. Use the fact that 4 directions are perpendicular to each other.

Step 1 : Find distances travelled by boats using the given rates. These distances are the two legs  of right triangle.

Distance = speed * time

First leg = 15 *3 = 45 miles

Second leg= 9*3= 27 miles

Using Pythagorean for  this right triangle, we find the longest side.

H^{2}=(45)^{2}+(27)^{2}

H^{2}=2754

H=\sqrt{2754}

H= 52.4785… ≈ 52.48 miles

After 3 hours , boats are 52.48 miles apart.

 

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