Question

Ava and Mary are 10 miles apart on a path when they start moving toward each other. Ava runs at a constant speed of 4 miles per hour, while Mary walks at a constant speed of 1 miles per hour. How long does it take until they meet?

Answer 1

Explanation:

You are after time. You know the total distance. They start off at the same time and meet after t hours

Let the meeting time = t

Let the distance from Mary's standpoint be d

Mary

d = r * t

r = 1 mile / hour

t = ?

Ava

d = r*t

d for Ava = 10 - d

r = 4 mile / hour

Solution

10 - d = 4 * t

The time is the same for both people

Ava: divide both sides by 4

10/4 - d/4 = t

Mary

d = 1 * t

d = t

10/4 - d/4 = d Add d/4 to both sides.

10/4 = d + d/4

10/4 = 5d / 4 Multiply both sides by 4

10 = 5d Divide both sides by 5

10/5 = 5d/5

d = 2

Since from Mary we have d = t

They will meet in 2 hours.