Name: Mr. Bollen

Who is asking: Teacher Level: Secondary

Question: Mr. Byrd leaves his house at 7:00am to go to work. If he drives 40 mph he will arrive 3 minutes late and if he drives 60mph he arrives 3 minutes early. At what speed will Mr. Byrd have to drive in order arrive exactly on time. Please describe how you arrived at your answer. Hint:(It's not 50mph)

On the midway point between Byrd's house and Byrd's office, there is a bridge. When Byrd drives at 40mph he arrives at the bridge a minute and a half late, and when he drives at 60mph he arrives there a minute and a half early. One solution would be for Mr. Byrd to drive up to the bridge at 40mph, and there speed up to 60mph to pick up the slack. That way he would always be on time.

We do not know the distance from the house to the office and this creates a complication. There are two way to overcome this complication, one that does not introduce a variable and a second which does introduce a variable.

But if Byrd sticks with this scheme for many weeks, at some point he will have driven in all 120 miles at 40mph from his home to the bridge, and 120 miles at 60mph from the bridge to the office. The 120 miles at 40mph will take in all 3 hours, and the 120 miles at 60mph will take in all 2 hours, for a total of 240 miles in 5 hours. What average speed is that?

Another way to proceed is to introduce a variable M for the number of miles from his house to the bridge. He than drives M miles at 40mph (which takes  ^M/₄₀ hours) and M miles at 60mph (which takes  ^M/₆₀ hours). Hence he travels a total of 2M miles in  ^M/₄₀ +  ^M/₆₀ = ^5M/₁₂₀ hours.