Question

Victor biked from his hometown to a neighboring city in 6 hours. He biked back to his hometown in 4 hours. His speed on the return trip was 4 mph faster than his speed on the first trip. How far apart are the two cities?

Answer 1

We will have the following:

His speed on the return (r) trio was 4mph faster than his speed in the first trip (o), so:

$r=o+4$

Then, we have that speed times distance equals time, and distance is equal to time over speed. Thus:

$6h(\frac{x}{\text{hours}})=4h(\frac{x+4}{\text{hours}})$

Then, we have:

$6x=4x+16\Rightarrow2x=16$$\Rightarrow x=8$

So, the initial speed was of 8mph.

Then we deternine the distance:

$d=(8mi/h)(6h)\Rightarrow d=48mi$

So, the two cities are 48 miles apart.