Nolan and Hugo started out at their houses and are biking towards each other. Nolan started out first, and has already gone 4 miles. He bikes at a constant speed of 2 miles per hour. Hugo just left, and rides at 3 miles per hour. When the boys meet halfway between their houses, they will continue to the park together. How long will that take? How far will each boy have ridden?

You can write these scenarios into equations:

y = distance (in miles)

x = the number of hours [you could put h instead of x, doesn't matter the variable]

Nolan

2x + 4 = y [rides 2 miles per hour (x), and had already gone 4 miles/is 4 miles in]

Hugo

3x = y [rides 3 miles per hour (x), and just started riding]

You can set these two equations equal to each other to find out when they meet: [this will first find how long it will take for them to meet]

2x + 4 = 3x You need to isolate/get x by itself, subtract 2x on both sides

2x - 2x + 4 = 3x - 2x

4 = x Now that you found x, you can use this to find y, you can use either equation to plug in 4 for x

3x = y

3 (4) = y

12 = y

2x + 4 = y

2 (4) + 4 = y

12 = y

x = 4 hours

y = 12 miles