### Answer to Problem of the Week

**Answer to the 9/17/2010 Problem of the Week**

Flying Flora is traveling an average speed of 76.4 miles per hour, rounded to the nearest tenth of a mile per hour.

**Solution:**

Let d = distance between Santa Fe and Las Cruces. So 2d = the distance for the round trip. To get the average speed for a trip with two or more “legs,” add up the distances to get total distance, then divide total distance by total time.

For this trip, we get the time for each “leg” by dividing the distance for the leg by the rate for the leg, using the formula, t = d/r. Traveling from Santa Fe to Las Cruces, Flying Flora’s time was d/105; traveling from Las Cruces to Santa Fe, her time was d/60. So the complete formula for average speed is given by: (2d) ÷ [(d/105) + (d/60)]. Solving this, the d-terms cancel out, and we are find that the expression simplifies to 76.3, with units of miles per hour. So the answer is

76.4 mph.

**The people who got this right —**

** **

Chris Mark

Irving Lubliner

Jeanine Rose

Sarah Gopher-Stevens

Congratulations to everyone who worked on the problem.

For anyone seeing this for the first time, the problem is this:

Flying Flora, late as usual for her business meeting, speeds from Santa Fe to Las Cruces at 105 mph. After arriving in Las Cruces, she gets an email alerting her that she was caught by a radar gun and received a speeding ticket (she knows the local DA; otherwise she would have been thrown in jail!). Much chastened, Flora drives back from Las Cruces to Santa Fe at just 60 mph. Your task: Without using a specific value for the distance between the towns, find Flying Flora’s average rate for the round trip. Please show your work and round off your answer to the nearest tenth of a mile per hour.