On the number line, a bug p is moving in the positive direction from the point 0, and a bug n is moving in the negative direction from the point 0. the speeds of both bugs are constant. both leave 0 at the same time, and four seconds later p has reached 12 and n has reached –8. chapter reference a if x is the point reached by p after t seconds, and y is the point reached by n after t seconds, express x and y in terms of t.

Bug P has moved to +12 in 4 seconds, so is moving +3 units in each second.
.. x = 3t

Bug N has moved to -8 in 4 seconds, so is moving -2 units in each second.
.. y = -2t


"per" means "divided by" (and vice versa), so -8 units per 4 seconds means
.. (-8 units)/(4 seconds) = -2 units/second . . . . . . . . reduce the fraction

When you multiply this fraction by a number of seconds, you cancel the "seconds" and the result is some number of units. For example,
.. (-2 units/second)*(4 second) = -8 units·second/second = -8 units
That is, speed multiplied by time gives distance.

In the equations above, we understand that the "3" means "3 units/second", and the "t" means "t seconds". Then when you multiply, the resulting x means "x units". The measures are usually left off and the equations are understood to give correct results when the variables have appropriate measures.

Cbecause they are equal so that means it is the same on both sides? ! hope this