Can a car go as fast in reverse as it does forward?

Q: Can cars go full speed in reverse?

Driving backward in Reverse Gear, you wont be able to drive any faster than like you are driving forward at low gear, because the transmission will not shift to any higher gears at REVERSE, you can step on gas to make your engine rpm go higher, it wont shift to higher gears.

They don't reach the same speed because of the gearbox.

You should take a look on how gearboxes work. Though there are some videos on YouTube, I'll give it a short try.

Your motor has a maximum round per minute count it can take without destroying itself, let's say a range from 1500 - 6000 rpm.

Now, what's gonna happen when we start the car and try to add this power to the wheels? Note: The car is still.
You connect the running engine at maybe 1500 rpm to the wheels and from one second to the other, the wheels will spin at a minimum of 1500 rpm.

1500 rpm on a wheel with a diameter of about 50 cm / 20 inches will turn it at about 135 km/h / 80mph. You definitely don't want to start a car with wheels spinning at this speed so therefore we need a solution.

A gearbox! Let's say 4 gears to drive and 1 to reverse.

The first gear will transfer the engines 1500 rpm at a ratio of maybe 25:1 (25 rotations of the engine will turn the wheel once). This will give a speed of about 5 km/h or 3 mph. A waaaay better way to get on moving.
Second gear might be a ratio of 15:1, third 5:1 and the fourth gear will provide the 1:1 ratio to reach higher speeds.

Then there's the reverse gear. It's quite the same as the first gear as the car will be standing. Again, we need a high ratio to start it slowly.
Let's choose 25:1 once again.

This means we can start at around 5km/h or 3 mph in reverse. Then we might want to speed up so we hit the throttle some more and reach the maximum of 6000 rpm. At 6000 rpm the wheel will spin at (6000 / 25, as the ratio is 25:1) 240 rounds per minute. This is a little more than 20 km/h or about 13 mph. The maximum speed this example car will go in reverse as we don't have a second or third reverse gear with a different gear ratio.

Some machines have a number of reverse gears, farming tractors for example.

NOTE: This is an 'explain it like I'm 5' approach, there are far more things to consider. For example: Most cars would just stall if you would try to start moving with the fourth gear in gear. Then there's a clutch etc...

Can cars go full speed in reverse?

Driving backward in Reverse Gear, you won't be able to drive any faster than like you are driving forward at low gear, because the transmission will not shift to any higher gears at REVERSE, you can step on gas to make your engine rpm go higher, it won't shift to higher gears.

What is the max speed of a car in reverse?

Cars have a dedicated gear to reverse, and this gear is just one. This means that while you are reversing in a car whether manual/automatic transmission, the car can't go beyond a certain speed that varies between 20-30 mph depending on the size of gear of the particular car.