SOLUTION: A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed o

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Question 1207807: A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.
Found 3 solutions by josgarithmetic, mananth, math_tutor2020:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
t hours
d distance between them
separating at right angle from each other

Car going east, distance 30t
Car going south, distance 40t

d%5E2=%2830t%29%5E2%2B%2840t%29%5E2

d=sqrt%28900t%5E2%2B1600t%5E2%29

d=t%2Asqrt%282500%29

highlight%28d=50t%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.
Let x(t): the distance the Neon has traveled east after t hours , speed = 30 mph
and y(t): the distance the truck has traveled south after t hours, speed 40 mph
x(t) =30t
y(t)=40t
d(t) = sqrt((30t)^2+(40t)^2) ( Pythagoras theorem)
d(t) = sqrt(900t^2+1600t^2)
d(t) = sqrt(2500t)
d(t) = 50t is the required expression

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

t = number of hours
The legs of the right triangle are 30t and 40t.
This represents the distance traveled by the Neon and the Mack truck respectively.

Plug a = 30t, b = 40t into c+=+sqrt%28a%5E2%2Bb%5E2%29 (a modified version of the Pythagorean theorem) to arrive at c = 50t

We have a right triangle with sides 30t, 40t, 50t.
This is based off the 3-4-5 Pythagorean triple.
Perhaps the most famous such triple.



Answer: 50t