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.