Carcass wrote:

Jake rides his bike for the first \(\frac{2}{3}\) of the distance from home to school, traveling at 10 miles per hour. He then walks the remaining \(\frac{1}{3}\) of the distance at 3 miles per hour. If his total trip takes 40 minutes, how many miles is it from Jake's home to his school?

A. \(\frac{5}{4}\)

B. \(\frac{15}{4}\)

C. 5

D. 6

E. 10

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 milesThen Jake walked for a distance of (1/3)D miles, which equals

D/3 milesTime = distance/rateSo, 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:

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