Question

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 ?

Answer 1

Answer: in 2/5 hours they will be at the same distance from their apartment.

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

Answer 2

Let the distance remaining after time t be x miles.

Distance traveled by Alan = (6-x) miles
Distance traveled by Soren = (8-x) miles

Time takes by the two is the same. Therefore,
(8-x)/12 = (6-x)/7 => 7(8-x) = 12(6-x) => 56-7x = 72-12x => 12x-7x = 72 -56 => 5x= 16 => x = 16/5 = 3.2 miles.

And then, time taken (t) = (8-3.2)/12 = (6-3.2)/7 = 0.4 hours