A woman drove to work at an average speed of miles per hour and returned along the same route at miles per hour. If her total traveling time was hour, what was the total number of miles in the round trip?
Let’s start with the obvious – it is not going to be 30 miles (because she drove part of the time faster and it took her an hour) and it is not 40 (because she drove for an hour and part of the time at lower speed than 40 miles per hour). Now, you might be tempted to answer 35. This is almost correct but it is not the right answer. If she drove for half an hour at 30 miles per hour and for half an hour at 40 miles per hour than the average speed would be 35 miles per hour – THIS ASSUMES THE TIME TRAVELED IS IDENTICAL !
In our case the distance traveled is identical – driving this distance at 30 miles per hour takes a little more than 1/2 an hour and driving the same distance at 40 miles per hour takes a little less – together these two times add up to an hour.
This means that if I had to guess I would choose 34 and 2/7 of a mile.
The woman drove from home to work – a distance of X miles – it took her then to get to work X/40 hours or (X/40)*60 minutes.
On the way back she drove the same distance – X at 30 miles per hour. This trip took her a longer time period to complete – it took her X/30 of an hour or (X/30)*60 minutes.
Together, back and forth, it took her an hour or 60 minutes.
X=120/7 or 17 and 1/7th of a mile.
We are looking on the entire distance or twice as many miles – 34 and 2/7th of a mile.