My husband and I recently purchased a home up the mountains, but I still commute down the hill 5 times a week for work. I am wondering if there are any driving tips/ tricks to save on gas / brakes. I have been told to shift down to 3rd gear when driving down hill to save your brakes, but it uses more gas. Now someone has recommended that I drive up the hill in 3rd gear to save the transmission. I have never heard of this and I enjoy listening to the show, so I thought I would ask for advice. Is shifting into 3rd beneficial when driving up hill?
You Forgot To Introduce Your Vehicle; Make, Model, Model-Year, And This Must Have A Manual Shift Transmission, Correct ?
What Size Is The Engine ? Do You Know ?
Which mountains ? Where Do You Live (Approximate Location) ?
How Long Does The Actual Mountain Portion Of The Driving Take ?
Most Owner’s Manuals cover this. Have you checked ?
CSA
As CSA suggested we need more information.
Downhill: the advice you received is probably good. Riding the brake can overheat the brake fluid and reduce stopping power greatly. Downshifting into a gear in which you can maintain the speed limit without using the gas pedal or the brake (other than in small amounts) is ideal on a long, steep downhill. You are using almost no gas–gravity is doing the work for you. Safety first, gas mileage second.
Uphill in automatic trans: I would let the trans pick the gear as it was designed to do unless the car is not running properly or well.
Uphill in manual: NEVER let the engine lug in too high a gear. 3rd gear on a 5 speed manual may be correct in this case. This is where we need more info.
In most modern cars w/electronic fuel injection, the injectors are completely shut off when coasting in gear. By using engine compression (3rd gear say) when going downhill, not only do you save wear and tear on your brakes, but you save gas too. If you coasted in neutral instead, using your brakes to slow down, you’d be using gas to keep the engine idling. As long as you don’t step on the gas pedal, you use no fuel at all going downhill in gear.
One thing to improve your car’s longetivity – if it’s feasible – is to drive downhill rather than uphill first thing in the morning. This gives the cold engine some time to warm up and get fully lubricated before putting a load on it by driving uphill.
The others have covered the gearing bit well, but I wanted to add another tip: When it dumps 3 feet of snow on the mountain, do not try to be a hero and get to work until the grader has cleared the road, even if that’s tomorrow. A couple of people tried to do this when they moved to my old mountain neighborhood and they almost drove off the side of the mountain. It’s a really good way to kill yourself.
If the road is extremely steep, 2nd or even low gear may be in order, up hill or down.
Also note that it may be sunny and the roadway may be clear on one side of the mountain, and shady and snow packed as you round a curve.
Thank you for your advice 
Ok so…
You Forgot To Introduce Your Vehicle; Make, Model, Model-Year, And This Must Have A Manual
Make: Dodge
Model: Neon
Year: 2005
Bought used w/ 29,000 miles in 2008 and no Manual.
Manual Trans.
What Size Is The Engine? 2.0 L/ 16 Valve
Which mountains? San Bernardino Mtns./ Crestline, CA
How Long Does The Actual Mountain Portion Of The Driving Take? 20 min.
My car now has just over 100,000 miles on it.