# Thread: Distance Problem *HELP*

1. ## Distance Problem *HELP*

hello everybody wondering if anybody can help me out with this one

- Mary drove from Amity to Belleville at a speed of 50mph. On the way back she drove 60mph. the total trip took 4 2/3 hours of driving time. what is the distance between the 2 cities?
D = RxT

Thanks for the help everybody.

2. Her total distance travelled is $\displaystyle 2.D$

Her average speed is $\displaystyle (50+60)/2 = 55$ mph

The total time is 4 2/3 hours or 4.67 hours

Therefore using the general formula distance=velocity x time,

$\displaystyle 2.D = 55$ x $\displaystyle 4.67$

$\displaystyle D = (55$ x $\displaystyle 4.67)/2$

$\displaystyle D = 128.43$ miles

3. Hello, Afterme!

Mary drove from Amity to Belleville at a speed of 50mph.
On the way back she drove 60mph.
The total trip took 4 2/3 hours of driving time.
What is the distance between the 2 cities?

$\displaystyle D \:= \:R \times T\quad\Rightarrow\quad T \:=\:\frac{D}{R}$

Going from A to B, Mary drove $\displaystyle D$ miles at 50 mph.
.Her time was: .$\displaystyle \frac{D}{50}$ hours.

Going from B to A, Mary drove $\displaystyle D$ miles at 60 mph.
. . Her time was: .$\displaystyle \frac{D}{60}$ hours.

Here total time was: $\displaystyle 4\frac{2}{3}\,=\,\frac{14}{3}$ hours.

There is our equation! . . . $\displaystyle \frac{D}{50} + \frac{D}{60} \;=\;\frac{14}{3}$

Got it?

4. I really appreciate it this guys. Thanks

5. For some reason, you get a slightly different answer between my way and Soroban's way. I think Soroban's way is correct - does that mean there is a flaw in my logic?

Just re-did this problem using different numbers with a known distance, and I can confirm that my logic is incorrect. Use Soroban's solution technique.