Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

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Question 153483: Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t: Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t
Answer by ankor@dixie-net.com(4538) About Me  (Show Source):
You can put this solution on YOUR website!
Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t.
:
You can see that the boats' paths represent 2 sides of a right triangle
The distance between the two boats is represented by the hypotenuse
:
Let t = travel time of the boats:
:
one boat dist = 22t, the other boat dist = 35t
;
d = sqrt((22t)^2 + (35t)^2)
:
d = sqrt((484t^2) + (1225t^2))
:
d = sqrt(1709t^2)
:
d = 41.34t
:
:
Check solution with calc using t = 1 hr
Enter: sqrt(22^2 + 35^2) = 41.34