Let's start with a word equation.

(time spent on bike) + (time spent walking) = 2/3 hours (= 40 minutes)

Let D = total distance (in miles) from home to school
So, Jake rode his bike for a distance of (2/3)D miles, which equals 2D/3 miles
Then Jake walked for a distance of (1/3)D miles, which equals D/3 miles

Time = distance/rate

So, we can write: (2D/3)/10 + (D/3)/3 = 2/3
Multiply both sides by 30 to get: 6D/3 + 10D/3 = 60/3
Multiply both sides by 3 to get: 6D + 10D = 60
Simplify: 16D = 60
Solve: D = 60/16 = 30/8 = 15/4

Answer: B

Cheers,
Brent