EDGE Math 8

Example 2

To go from his house to his office, Mr. Cruz drives a distance of 12 km at a speed of y km/h. To go back from his office to his house, he uses the same route and drives at a speed of 5 km/h faster than going from his house to his office.

a. Express Mr. Cruz's average speed for his round-trip using a rational expression.
b. Determine Mr. Cruz's average speed for the round-trip if his speed in going from his house to his office is 60 km/h.

Solution

Recall the following formulas:

distance = speed

\times

time

time = distance

\div

speed

a. You can find the average speed of Mr. Cruz's round-trip by dividing the total distance traveled for the round-trip by the total time of travel.

average speed= \frac{total distance}{total time}

= \frac{12 + 12}{\frac{12}{y} + \frac{12}{y + 5}}

= \frac{24}{\frac{12 (y + 5) + 12 y}{y (y + 5)}}

= 24 \cdot \frac{y (y + 5)}{12 (y + 5) + 12 y}

= 24 \cdot \frac{y (y + 5)}{12 (y + 5 + y)}

= \frac{2 \cdot 12 y (y + 5)}{12 (y + 5 + y)}

= \frac{2 y (y + 5)}{2 y + 5}

Hence, the average speed of Mr. Cruz's round-trip is $\frac{2 y (y + 5)}{2 y + 5}$ km/h.

b. Substitute 60 for y in the rational expression $\frac{2 y (y + 5)}{2 y + 5} .$

\frac{2 y (y + 5)}{2 y + 5} = \frac{2 (60) (60 + 5)}{2 (60) + 5}

= \frac{120 (65)}{125}

= \frac{312}{5} or 62.4

Thus, if Mr. Cruz's speed from his house to his office is 60 km/h, his average speed for the round-trip is 62.4 km/h.

Problems Involving Rational Expressions