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, runs faster. - alberto maintains a speed of 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. - the first person to cross the finish line is. the first person to cross the finish line is.

Explanation:

Step1: Compare early race speeds

Look at the first hour: Alberto reaches 20 km, Bianca reaches <5 km. Alberto's slope is steeper, so he runs faster early.

Step2: Calculate Alberto's 1st hour speed

Speed = $\frac{\text{Distance}}{\text{Time}} = \frac{20\ \text{km}}{1\ \text{h}} = 20\ \text{km/h}$

Step3: Analyze Bianca's speed trend

Bianca's curve gets steeper over time, so her speed increases.

Step4: Identify finish line winner

Alberto stops at 20 km for hours; Bianca reaches 50 km first, then Alberto later.

Answer:

• Early in the race, Alberto runs faster.
• Alberto maintains a speed of $\boldsymbol{20}$ km/h during the first hour of the race.
• Meanwhile, Bianca's running speed increases.
• The first person to cross the finish line is Bianca.