Answer: in 2/5 hours they will be at the same distance from their apartment.
Step-by-step explanation:
The data that we have is:
Alan works 6 miles away from the apartment, and his speed is 7 miles per hour.
Soren works 8 miles away from the apartment, and his speed is 12 miles per hour.
We can calculate the distance as a function of time by the equation.
D = initial distance - speed*t
where t is the number of hours; so we have that the equation for Allan is:
Da = 6 mi - 7 mi/h*t
The equation for Soren is:
Ds = 8mi - 12mi/h*t
They will be at the same distance to the apartment when Da = Ds, so we must have that:
6mi - 7mi/h*t = 8mi -12mi/h*t
we need to solve it for t.
(12mi/h - 7mi/h)*t = 8mi - 6mi
5mi/h*t = 2mi
t = (2/5)h