Algebra Know-It-ALL

Adding x to each side produces

100 = 7 x

Dividing through by 7, we find that x= 100/7. We can plug this into the second original

equation to get

y= 6 × 100/7

= 600/7

The two numbers are 100/7 and 600/7. We can also express them in whole-number-and-

fraction form as 14-2/7 and 85-5/7.

3. The process for solving this problem is rather long and a little tricky as well! Let x be the
   speed of the ball relative to the car. Let y be the speed of the car relative to the pavement.
   When you throw the first baseball straight out in front of the car, the ball’s speed adds
   to the car’s speed, so the ball moves at a speed of x+y relative to the pavement. That’s
   simple enough! When you throw the second ball straight backward, the ball’s speed sub-
   tracts from the car’s speed, so the ball moves at a speed of y−x relative to the pavement.
   When the second ball hits the pavement, it’s moving backward, opposite to the motion
   of the car. Therefore, we must consider the direction of the motions relative to the pave-
   ment. Let’s define forward motion relative to the pavement (that is, in the direction of the
   car) as positive speed, and backward motion relative to the pavement (opposite to the car’s
   motion) as negative speed. Keep in mind that these definitions apply only to motions that
   are observed with respect to the pavement.
   The equations describing the movement of the ball relative to the pavement can be
   written out:

x+y= 135

when for the ball you throw straight out in front of the car, and

y−x=− 15

for the ball you throw straight out behind the car. The speed in the second case is negative

because the ball hits the pavement moving backward. When we morph these two equa-

tions into SI form, we obtain

y=−x+ 135

and

y=x− 15

When we mix the right sides, we get

−x+ 135 =x− 15

Chapter 16 639