# Friends Meeting on Bikes

## Task

Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bikes and meet in between. One day they left their houses at 8 am and met at 11 am. Taylor rode at 12.5 miles per hour. How fast did Anya ride?

## IM Commentary

There is a more scaffolded version of this same problem; see 6.RP.3 Friends Meeting on Bicycles.

Additional questions for a student who doesn't know where to start: "How long did the bike ride take? How far did Taylor ride? How far did Anya ride?"

Comparing the solutions below using distance and using speed, there is an opportunity to point out the distributive property. If we take "8.5 mph + 12.5 mph = 21 mph" and multiply by 3 hours, we get "63 miles = 25.5 miles + 37.5 miles"

## Solutions

Solution: Finding distances first

Since the bike ride took 3 hours, Taylor must have ridden 37.5 miles. Therefore Anya must have ridden 63 - 37.5 - 25.5 miles. If we divide the distance Anya rode by the amount of time it took her to ride, we will get her speed (assuming she rode at a constant speed). $$25.5 \text{ miles } \div 3 \text{ hours } = 8.5 \text{ miles per hour}.$$

So if Anya rode at a constant speed, she was traveling 8.5 miles per hour.

Solution: Subtracting Taylor's speed from total speed

The distance between the two friends is decreasing by $$63\text{ miles }\div 3\text{ hours }= 21\text{ miles per hour}.$$ Since Taylor rides at 12.5 miles per hour, Anya's speed must be 21 - 12.5 = 8.5 miles per hour.

Assuming Anya rode at a constant speed, she was traveling 8.5 miles per hour.

## Friends Meeting on Bikes

Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bikes and meet in between. One day they left their houses at 8 am and met at 11 am. Taylor rode at 12.5 miles per hour. How fast did Anya ride?