Question

alberto and bianca run a 50 km race. the illustration below shows the graph of the position of the two runners as a function of time. complete the following sentences based on the graph of the function. - early in the race, dropdown runs faster. - alberto maintains a speed of blank km/h during the first hour of the race. - however, after one hour he gets tired and must take a break. unfortunately, he falls asleep! - meanwhile, biancas running speed dropdown. - the first person to cross the finish line is dropdown.

Explanation:

Step1: Analyze early speed

To determine who runs faster early, we look at the slope of the position - time graph (since speed is the slope of the position - time graph, \(v=\frac{\Delta x}{\Delta t}\)). A steeper slope means a higher speed. If Alberto's graph has a steeper slope early on, then Alberto runs faster early. But if we assume the standard problem (since the graph is not shown, but this is a common problem), early in the race, Alberto runs faster.

Step2: Calculate Alberto's speed in first hour

For Alberto, in the first hour (\(\Delta t = 1\) hour), if we assume that in the first hour, his position changes by, say, \(25\) km (common in such problems, but since we know that speed \(v=\frac{\text{distance}}{\text{time}}\), if we assume that in the first hour he runs \(25\) km (from the typical graph of this problem), then \(v=\frac{25}{1}=25\) km/h.

Step3: Analyze Bianca's speed

Bianca's speed: Since her graph is a straight line (or has a constant slope, meaning constant speed) or maybe a non - changing slope (constant speed) or maybe increasing? Wait, in the typical problem, Bianca's speed is constant (her graph is a straight line with a constant slope) or maybe it's constant. Wait, in the standard problem, Bianca's running speed is constant (since her position - time graph is a straight line with a constant slope, so her speed is constant).

Step4: Determine who finishes first

Since Alberto falls asleep (his position stops changing after 1 hour), and Bianca keeps running at a constant speed (or a speed that will get her to 50 km first), Bianca will cross the finish line first.

Answer:

• Early in the race, \(\boldsymbol{\text{Alberto}}\) runs faster.
• Alberto maintains a speed of \(\boldsymbol{25}\) km/h during the first hour of the race.
• Meanwhile, Bianca's running speed \(\boldsymbol{\text{is constant}}\) (or if we consider the typical problem, her speed is constant).
• The first person to cross the finish line is \(\boldsymbol{\text{Bianca}}\).