Two people start walking at the same time in the same direction. One person walks at 7 mph and the other person walks at 4 mph. In how many hours will they be 0.75 mile(s) apart?

It'll take them 0.25 h or 15 minutes to be 0.75 miles apart at that speed.

Step-by-step explanation:

In these case we have two people that are moving in the same direction, so in order to calculate how the distance between them changes as time progress we need to calculate the relative velocity between them. When they are walking in the same direction we should subtract the greater velocity from the lesser one and when they are walking in oposite directions we should sum the velocity. In this case we need to subtract, so we have:

relative velocity = 7 - 4 = 3 mph

Since we want to know the time that they should walk in that speed in order to be separated by 0.75 miles we can use the equation bellow that describes the distance travelled in a constant velocity movement.

S = So + v*t

Where S is the final distance, So is the initial distance, v is the velocity and t is the elapsed time. We want to solve for time, so we should isolate it in the equation:

v*t = S - So

t = (S - So)/v

We assume that when they start the walking their distance is 0, so we have:

t = (0.75 - 0)/3 = 0.25 h

It'll take them 0.25 h or 15 minutes to be 0.75 miles apart at that speed.

t= 0.25 hours

Step-by-step explanation:

If the two people start walking in the same direction from a point,

their distances apart will be the difference of their distance from the starting point.

Let t be the time when they will be 0.75 miles apart

The difference of their distances = 7t-4t =3t

Therefore:

3t=0.75

t = 0.75/3

t= 0.25 hours

In 0.25 hours, they will be 0.75 miles apart.

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5