Annette drives her car 120120 miles and has a mean of a certain speed. if the mean speed had been 3mph3⁢mph more, she could have traveled 128128 miles in the same length of time. what was her mean speed?

So Annette's speed was 45 mph.

Let's make 2 equations to represent Annette's speed.

T*S = 120
Where
T = the time Annette has been driving.
S = her mean speed.
120 = number of miles she's traveled.

and another equation that's
T*(S+3) = 128

So we now have 2 equations with 2 unknowns. They are
T*S = 120
T*(S+3) = 128

Let's divide the top equation by S on both sides and the bottom equation by (S+3) on both sides giving
T = 120/S
T = 128/(S+3)

So we now know that 120/S is equal to 128/(S+3). So let's make that equation and solve for S
120/S = 128/(S+3)

Multiply both sides by S(S+3)
120(S+3) = 128S

Distribute the 120 on the left
120S + 360 = 128S

Subtract 120S from both sides
360 = 8S

And divide both sides by 8
45 = S

So Annette's speed was 45 mph.