Question

The following steps show how the equation for the average rate can be transformed so that it is written in terms of only the rates for each leg of the trip. Write an algebraic justification for each step. Think about the number operations and properties that you know.

Answer 1

Step 1:
Sum of fractions in the denominator making cross product:
d / r1 + d / r2
Resulting:
d * r2 + d * r1 / (r1 * r2)
Step 2:
Multiply numerator and denominator by the following expression:
(r1 * r2) / (d * r2 + d * r1)
Step 3:
Take common factor in the denominator of the expression in step 2.
Resulting:
(d * r2 + d * r1) = d * (r2 + r1)