# Trisha and Gordon drive away from a campground at right angles to each other. Trisha's speed is 70mph and Gordon's speed is 55mph. Express the distance between the cars as a function of time.

steveschoen | Certified Educator

Hi, Iro1979,

First, we need to determine the distance each travel.  Since we aren't sure how long that is, we use:

t = time travelled in hours

You can assume they started travelling at the same time.  So, the distance one travels would be:

D1 = v1t

D1 = 70t

And, for the other one:

D2 = 55t

When we lay these out on paper, we would have a right triangle.  And, the problem would be asking us to find the hypotenuse.  So, we would have:

D = √(D12 + D22)

D = √((70t)2 + (55t)2)

D = √(4900t2 + 3025t2)

D = √(7925t2)

So, D would be (√7925)t, or approximately 89.02t.

Good luck, Iro1979.  I hope this helps.

sciencesolve | Certified Educator

You need to use distance equation such that:

`v = d/t => d = v*t`

`v` represents the velocity

`d` represents the distance between cars

You need to evaluate the velocity using the information provided by the problem, such that:

`v = sqrt(v_x^2 + v_y^2) => v = sqrt(55^2 + 70^2)`

`v = sqrt(3025 + 4900) => v = sqrt(7925)`

`f(t) = sqrt(7925)*t`

Hence, expressing the distance between cars as a function of time yields `f(t) = sqrt(7925)*t.`