When you put the car in overdrive and take off it speeds up to 45mph and starts to rev up and not go any faster. What could this be?

Overdrive acts like a final gear. It's easily noticed if it is on or off when cruising at higher speeds, as when operating the switch you will notice the engine revs alternate between higher and lower rev ranges.
When the engine revs drop, then overdrive is on, and when they rise, then it is effectively off.

The overdrive function works just like any other gear in that it reduces the torque from the engine to the wheels, and allows the engine speed to drop. This isn't always beneficial when climbing hills or towing however, or when driving hard, as you may prefer that the gearbox wasn't always changing gear into overdrive, as overdrive reduces the torque from the engine as a means to increase fuel economy and reduce stress. It is for this reason that the overdrive can be disengaged, effectively reducing the number of gears in the gearbox which you have available to you.

So simply put, for most drivers, in most circumstances, they will not need to turn the overdrive off.

In answer to the light on/off, the majority of vehicles have overdrive in the 'OFF' position when the light is on. It's a reminder light (amber) that you likely aren't employing the best fuel saving technique.

at speed ( above 45MPH ) the engine RPM will increase when shifting the overdrive "off"

conversely when at speed and you turn overdrive "on" the RPMs will decrease

overdrive is for highway driving, lowers your engine rpm's and saves gas-allows the engine to not work as hard at higher speeds. Not desirable in around town traffic, and if you can lock it out if you do most driving under 45mph, a good idea so you don't 'lug' your engine.

Hi and welcome to FixYa!
It's not wise to drive on overdrive everytime. When you are cruising that's when OD should beused.

Hope this helps and thank you for using FixYa! Have a good one!

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It will shift out of overdrive upon increasing throttle , pulling hills and so on. Your overdrive probably kicks in around 35 to 45mph and kicks back out as you increase throttle. Electrically controled speed sensor to control the response. Overwise the engine would bog down to a stall. Over drive is just that. It changes the gearing ratio to over drive meaning less then final gear 4 to 1 down to 4 to 3 etc more direct drive ratio to lessen consumtion of fuel with less stress on engine. Have shift speed sensor adjusted. Don't drive in overdrive in city if most driving is under 45mph

Check your transmission fluid level and/or have the fluid changed. If problem persist have a transmission professional at a dealership or transmission shop service it.

First check fluid level. Low fluid leads to hot burnt clutches in the transmission and bad shifting. May want to change the fluid and filter altogether. If this doesnt help than a modulator on the transmission along with being old and worn out may be leading to failure.

There isn't anything wrong with your car. This is perfectly normal. I have a 2000 ES300 as well as other people that I know and it operates in the same way. Overdrive doesn't mean the same thing for every car or transmission. In our case overdrive is simply a reference to the top gear which is 4th gear. When you switch overdrive off(which is depressing the button causing the O/D OFF dash light to illuminate,) the highest gear becomes 3rd because you turned 4th gear or overdrive off. The application scenario for this is usually mountainous terrain where a lot of uphill driving makes it more feasible not to up shift into 4th gear while ascending and descending. It will not switch back to overdrive or 4th gear until you re-engage it by turning the overdrive back on or repressing the button. Again, when the O/D OFF dash light is illuminated, overdrive which is 4th gear is off and the highest gear will then become 3rd. It will never shift into 4th gear while this light is illuminated or overdrive is off. When you press the button and the O/D OFF dash light is NOT illuminated overdrive is on and therefore it will shift into 4th gear as usual. This applies to all 97-2001 ES300's and probably any other car you drive tat exhibits this same type of change when overdrive is turned off.