Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

Statement #1: If she had driven 50% faster, her new time would have been 2/3 of her original time.

Statement #2: If she had driven 20 mph faster, she would have arrived an hour sooner.

Answer:
Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

Let's say the original variables are D = 120, R, and T, and the original case is 120 = RT.

Statement #1: If she had driven 50% faster, her new time would have by 2/3 of her original time.

To increase by 50%, we will multiply by the multiplier 1.5. This means that the new speed, R2, is R2 = 1.50*R = (3/2)*R. The new time is T2 = (2/3)*T. Well, we know, that 120 = (R2)*(T2) --- the new speed and time must have the small product as the original speed and time. 120 = (R2)*(T2) = [(3/2)*R]*[(2/3)*T] = (3/2)*(2/3)*RT = RT. This information leads in a big logical circle right back to the original equation 120 = RT. It gives us no new information at all. Therefore, this statement, by itself, does not provide any insight into the answer to the prompt question. This statement is insufficient.

Statement #2: If she drove 20 mph faster, she would have arrived an hour sooner.

Now, we know R2 = R + 20 and T2 = T - 1. Again, we know that 120 = (R2)*(T2), so

120 = (R + 20)*(T - 1) = RT - R + 20T - 20

120 - RT = 0 = 20T - R - 20

That is one equation with two unknowns, and 120 = RT is a second equation with two unknowns. We have two clearly different equations for the two unknowns, so even without solving, this is sufficient to determine a unique value for the variables R & T.

Answer = (B)

I don't understand the second part. we cant solve the equations 120=RT and 120-RT=0=20T-R-20

20T-R=20 this just 1 equation and two unknowns[/b]