# Find Distance

#### harpazo

##### Pure Mathematics
Banned
Molly drives to a destination at a rate of sixty miles per hour. She drives back over the same route at a rate of forty miles per hour due to traffic. If the round trip takes two hours, how far is the destination?

Solution:

D = rt

Going Rate = 60 mph
Returning Rate = 40 mph

Going:

D_1 = 1(60)

D_1 = 60 miles

Returning:

D_2 = 1(40)

D_2 = 40 miles

Yes? No?

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
No...it appears you are assuming she takes 1 hour going there and 1 hour coming back. I would let $$t$$ be the time it took to get there and so $$2-t$$ will be the time it takes to get back...:

$$\displaystyle d=60t=40(2-t)\implies t=\frac{4}{5}\implies d=48\text{ mi}$$

• anemone and harpazo

#### harpazo

##### Pure Mathematics
Banned
No...it appears you are assuming she takes 1 hour going there and 1 hour coming back. I would let $$t$$ be the time it took to get there and so $$2-t$$ will be the time it takes to get back...:

$$\displaystyle d=60t=40(2-t)\implies t=\frac{4}{5}\implies d=48\text{ mi}$$
What's wrong with my reasoning?

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
• anemone and harpazo

#### harpazo

##### Pure Mathematics
Banned
Math is very humbling. This is a middle school math question.

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
We know distance is speed times time:

$$\displaystyle d=vt$$

Now suppose we are given two different speeds for the same distance:

$$\displaystyle d=v_1t_1=v_2t_2$$

If we assume $$\displaystyle t_1=t_2$$ then it follows that we must also have $$\displaystyle v_1=v_2$$. So, when we travel a certain distance, if speed changes, then so must the time it takes to cover that distance. If we double our speed, then the time it takes to cover the distance is cut in half, etc.

• anemone and harpazo

#### harpazo

##### Pure Mathematics
Banned
We know distance is speed times time:

$$\displaystyle d=vt$$

Now suppose we are given two different speeds for the same distance:

$$\displaystyle d=v_1t_1=v_2t_2$$

If we assume $$\displaystyle t_1=t_2$$ then it follows that we must also have $$\displaystyle v_1=v_2$$. So, when we travel a certain distance, if speed changes, then so must the time it takes to cover that distance. If we double our speed, then the time it takes to cover the distance is cut in half, etc.
Can you post and solve a word problem to show this fact?