Algebra Demystified 2nd Ed

436 algebra De mystif ieD

If we need to find the distance between two bodies traveling at right angles

away from each other, we must use the Pythagorean theorem, a^2 + b^2 = c^2 in

combination with the distance formula, D = rt. We use the distance formula to

represent the lengths of sides of a right triangle. For example, if a car is traveling

60 mph, then the length that it has traveled is 60t miles, where t is in hours.

Because the bodies are traveling at right angles to each other, their paths form

two sides of a right triangle and the distance between them represents the

hypotenuse of the right triangle. This is where the Pythagorean theorem comes

in, with a and b representing the distance traveled by each body (in terms of t)

and c representing the distance between them.

EXAMPLE

A car passes under a railway trestle at the same time a train is crossing the

trestle. The car is headed south at an average speed of 40 mph. The train is

traveling east at an average speed of 30 mph. After how long will the car

and train be 10 miles apart?

Let t represent the number of hours after the train and car pass each

other. (Because the rate is given in miles per hour, time must be given in

hours.) The distance traveled by the car after t hours is 40t and that of the

train is 30t.

c =1 0

b =3 0 t

a =4 0 t (40ta) (^2 2) + (30 + b^2 t= ) 2 c=1^202
FIGURE 11-5
EXAMPLE
A car passes under a railway trestle at the same time a train is crossing the
trestle. The car is headed south at an average speed of 40 mph. The train is
EXAMPLE
A car passes under a railway trestle at the same time a train is crossing the