# another word prob: Juan drove 80 miles at an average rate of

#### frenzy_252003

##### New member
Juan Rivera drove 80 miles into the country at an average rate of 55 mi/h. He drove back on the same highway at an average rate of 45 mi/h. What was his average rate of speed for the entire round trip? (hint : the answer is not 50 mi/h)

#### soroban

##### Elite Member
Re: yay.. another word problem.. thanks!

Hello, frenzy_252003!

This is a classic "trick question" . . .

Juan Rivera drove 80 miles into the country at an average rate of 55 mph.
He drove back on the same highway at an average rate of 45 mph.
What was his average rate of speed for the entire round trip?
(Hint : the answer is not 50 mph)

$$\displaystyle \text{(Average speed) } = \frac{\text{(total distance)}}{\text{(total time)}}$$

Juan drove out 80 miles at 55 mph . . . This took $$\displaystyle \frac{80}{55}\,=\,\frac{16}{11}$$ hours.

Then he drove back 80 miles at 45 mph . . . This took $$\displaystyle \frac{80}{55} \,=\,\frac{16}{9}$$ hours.

His total time was: $$\displaystyle \,\frac{16}{11}\,+\,\frac{16}{9}\:=\:\frac{320}{99}$$ hours.

His total distance was: $$\displaystyle \,80\,+\,80\:=\:160$$ miles.

Therefore, his average speed was: $$\displaystyle \L\:\frac{160}{\left(\frac{320}{99}\right)} \:=\:\fbox{49.5 \text{ mph}}$$