Question

anna took a bus tour of new york city during summer vacation. her friend, gabby, took a bus tour of san francisco. these graphs show the distance each tour traveled over time.
new york city tour
san francisco tour
complete the table. answer each question by selecting one or both tours.
which tour lasted 60 minutes?
which tour covered more distance in the interval from ( t = 0 ) to ( t = 18 ) than in the interval from ( t = 18 ) to ( t = 24 )?
which tour covered a distance of 20 miles?
which tour stopped for a period of time?

Explanation:

Step1: Check the time - axis for 60 minutes

For the New York City tour, the \(x\) - axis (time) goes up to 60 minutes. For the San Francisco tour, the \(x\) - axis also goes up to 60 minutes.

Step2: Analyze the distance for \(t = 0\) to \(t=18\) and \(t = 18\) to \(t = 24\) for New York City tour

For the New York City tour:

• From \(t = 0\) to \(t = 18\), the distance goes from \(d = 0\) to \(d = 10\). The change in distance \(\Delta d=10 - 0=10\)
• From \(t = 18\) to \(t = 24\), the distance remains \(d = 10\). The change in distance \(\Delta d=10 - 10 = 0\)

For the San Francisco tour:

• From \(t = 0\) to \(t = 18\), the distance goes from \(d = 0\) to \(d = 4\). The change in distance \(\Delta d=4 - 0=4\)
• From \(t = 18\) to \(t = 24\), the distance goes from \(d = 4\) to \(d = 6\). The change in distance \(\Delta d=6 - 4=2\)

Step3: Check the distance - axis for 20 miles

For the New York City tour, the \(y\) - axis (distance) goes up to 19 miles. For the San Francisco tour, the \(y\) - axis goes up to 20 miles.

Step4: Check for a horizontal line (stopping)

A horizontal line in a distance - time graph means the distance is not changing (the object is stopped). The New York City tour has a horizontal line from \(t = 18\) to \(t = 24\)

Answer:

• Which tour lasted 60 minutes? Both tours
• Which tour covered more distance in the interval from \(t = 0\) to \(t = 18\) than in the interval from \(t = 18\) to \(t = 24\)? New York City tour
• Which tour covered a distance of 20 miles? San Francisco tour
• Which tour stopped for a period of time? New York City tour