Alan works 6miles away from the apartment and rollerblades from his work place to the apartment at a constant rate of 7miles per hour . soren works 8 miles away from the apartment and bikes from his work place at a constant rate of 12miles per hour . how much time in hours do alan and soren have to travel to be the same distance from their apartment ?

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

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490