A few days ago I heard someone at the running club talking about a hilly course, “You’ll be slower on the uphills, but you’ll make up the on the downhills“. This reminds me of a problem I gave to a friend that was studying for her GRE a couple of years ago. She’s an accomplished triathlete, so I posed the following problem:
You’re going on a 60 mile bike ride with friends, and you tell them you’re going to average 20 mph. However, you have a headwind on the first half and only average 15 mph for this part. You have a tailwind on the way back, so how fast do you have to ride so that you average 20 mph for the whole ride?
Here’s the easy way to think about it. To average 20 mph, you have to do the ride in 3 hours. If the first half (30 miles) is at 15 mph, then you took 2 hours. This means you have an hour left to finish your ride – you have to ride back at 30 mph. You lost 5 mph on the way there, but have to ride 10 mph faster on the way back. Ain’t gonna happen!
So, you won’t make your 20 mph average. Same goes for hills when you’re running. Or fuel when you’re flying an airplane – the penalty of the headwind won’t be caught up on the way back.
