Plugging In: Avoiding Bad Numbers
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time, they are driving toward each other and are 60 miles apart. One and a half hours later, they are again 60 miles apart, driving away from each other. If Otto drives at a speed of $$x$$ miles per hour, then, in terms of $$x$$, what is Han's driving speed, in miles per hour?
__Plug In__ $$x=20$$ into the answer choices, and __POE__ those that do not match 60.
Only answer choice A, $$80-x$$, gives you the goal:
>$$80 - x = 80-20 = 60$$.
All the other answer choices do not match 60 for this Plug-In, so this is the right answer choice.
Incorrect.
[[snippet]]
If you __Plug In__ $$x=20$$ into this answer choice, then you get
>$$80-2x = 80-2(20) = 40$$.
This does not match the goal from the __Speed Table__. __POE__ this answer choice and move on.
Incorrect.
[[snippet]]
If you __Plug In__ $$x=20$$ into this answer choice, then you get
>$$40-x = 40-20 = 20$$.
This does not match the goal from the __Speed Table__. __POE__ this answer choice and move on.
Incorrect.
[[snippet]]
If you __Plug In__ $$x=20$$ into this answer choice, then you get
>$$120-x =120-20 = 100$$.
This does not match the goal from the __Speed Table__. __POE__ this answer choice and move on.
Incorrect.
[[snippet]]
If you __Plug In__ $$x=20$$ into this answer choice, then you get
>$$\displaystyle 40-\frac{x}{2} = 40-\frac{20}{2} = 30$$.
This does not match the goal from the __Speed Table__. __POE__ this answer choice and move on.
Correct.
[[snippet]]
In this case, the __Speed Table__ is as follows:
| | Speed | Time | Distance |
|------|-------------------|-----------|----------|
| Otto | $$\color{green}{x = 20}$$ | $$\frac{3}{2}$$ | $$30$$ |
| Han | $$\displaystyle \color{red}{\frac{90}{\frac{3}{2}} = 60}$$ | $$\frac{3}{2}$$ | $$90$$ |
Thus, your __goal__ is 60.
$$80-x$$
$$40-x$$
$$80-2x$$
$$120-x$$
$$40-\frac{x}{2}$$
Continue
