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Two cars leave an intersection at the same time. One is headed south at a constant speed of 40 miles per hour, the other is headed west at a constant speed of 30 miles per hour (see the figure). Express the distance d between the cars as a function of the time t. (Hint: At t = 0 the cars leave the intersection.)


d(t)= ...?

Verified Answer :

AL2006

I got into a mess of trouble when I reached the part where it says
"(see the figure)".  But I think I was able to get enough out of the
rest of the question to answer it.

One car is headed south, and the other car is headed west.
So the cars are driving on the legs of a right triangle, and the
hypotenuse is always the line between the cars.

First car:  Distance from the starting point after 't' hours = 40 t miles.

Second car:  Distance from the starting point after 't' hours = 30 t miles.

         Distance between the cars

      = hypotenuse of the right triangle

     =  √(one leg² + other leg²)

     =  √[ (40t miles)² + (30t miles)² ]

     =  √ (1600t² miles² + 900t² miles²)

     = √   2500 t² miles²

      d(t) = 50 t miles . 

The cars are 50 miles apart after 1 hour, 100 miles apart after 2 hours,
150 miles after 3 hours, 200 miles after 4 hours, . . . , etc.

syed514

after t the first car 30t the second 40t 


you have a right triangle 

d^2=(30t)^2+(40t)^2=2500t^2 

d=sqrt(2500t^2)=50t