Walking at 4 mph, a person covers a certain distance in a given time. If he increases his speed to 9 mph, he covers 7.5 miles more in the same time. How much distance does he cover originally?

$$ speed = \frac{distance}{time} $$

Walking at 4 mph, a person covers a certain distance in a given time.

let the distance be d and time t

$$ 4 mph = \frac{d}{t} $$...............(1)

If he increases his speed to 9 mph, he covers 7.5 miles more in the same time

$$ 9 mph = \frac{d + 7.5}{t} $$...................(2)

from (1) and (2)

$$ \frac{d}{4} = \frac{d + 7.5}{9} $$

solving $$ d = \frac{30}{5} = 6 miles $$