Question

jim began a 155 - mile bicycle trip to build up stamina for a triathlete competition. unfortunately, his bicycle chain broke, so he finished the trip walking. the whole trip took 5 hours. if jim walks at a rate of 3 miles per hour and rides at 43 miles per hour, find the amount of time he spent on the bicycle.
jim rode for \\(\square\\) hours

Explanation:

Step1: Define Variables

Let \( t \) be the time (in hours) Jim spent riding the bicycle. Then the time he spent walking is \( 5 - t \) hours (since the total trip took 5 hours).

Step2: Set Up Distance Equation

The distance ridden is \( \text{rate}_{\text{ride}} \times \text{time}_{\text{ride}} = 43t \) miles. The distance walked is \( \text{rate}_{\text{walk}} \times \text{time}_{\text{walk}} \). Wait, the walking rate seems to have a typo, but assuming it's 3 miles per hour (from the partial text), the distance walked is \( 3(5 - t) \) miles. The total distance is 155 miles, so:

$$ 43t + 3(5 - t) = 155 $$

Step3: Solve the Equation

Expand the equation:

$$ 43t + 15 - 3t = 155 $$

Combine like terms:

$$ 40t + 15 = 155 $$

Subtract 15 from both sides:

$$ 40t = 140 $$

Divide both sides by 40:

$$ t = \frac{140}{40} = 3.5 $$

Answer:

\( 3.5 \)