Question

Julian rides his bike uphill for 45 minutes, then turns around and rides back downhill. It takes him 15 minutes to get back to where he started. His uphill speed is 3 miles per hour slower than his downhill speed. Find Julian’s uphill and downhill speed.

Answer 1

uphill speed = 1.5 mph, downhill speed = 4.5 mph

Step-by-step explanation:

We are asked to find Julian’s uphill speed and downhill speed. Let’s let r represent Julian’s uphill speed in miles per hour. In 45min=34hr, he rides uphill a distance rt=34r miles. Since his downhill speed is 3 miles per hour faster, we represent that as r+3. In 15min=14hr, he rides downhill a distance (r+3)t=r+34 miles. We can set these distances equal to find

34r=r+34

Multiplying both sides by 4 and then subtracting r from both sides yields

3r2r=r+3=3

Solving for r=32, Julian’s uphill speed is 1.5 miles per hour and his downhill speed is r+3=4.5 miles per hour.

Answer 2

1.5mi/hr, 4.5mi/hr

Step-by-step explanation:

Given:

45 min = 0.75h, 15 min = 0.25h

(1) 0.75v₁ = 0.25v₂

(2) v₁ = v₂ - 3

Solve for v₁ and v₂:

0.75(v₂ - 3) = 0.25v₂ = 0.75v₂ - 2.25 = 0.25v₂

0.5v₂ = 2.25

v₂ = 4.5

v₁ = 1.5