Question

the graph shows the relationship between the number of cars on a certain road and the time of day for times between 5:00 a.m. and 9:00 a.m. complete parts (a) and (b) below.

a. what was the increase in the number of cars on the road between 6:00 a.m. and 6:30 a.m.?

(type a whole number.)

b. during which half hour was the increase in the number of cars the greatest?

a. 7:00 - 7:30
b. 8:30 - 9:00
c. 6:00 - 6:30
d. 5:00 - 5:30

(graph: title: traffic patterns, x - axis: # of cars (300, 400, 500, 600, 700, 800, 900), y - axis: time (5am, 6am, 7am, 8am, 9am), with a red line plot showing traffic over time.)

Explanation:

Part (a)

Step1: Identify values at 6:00 and 6:30

At 6:00 A.M., the number of cars (from the graph) is 400. At 6:30 A.M., we assume (from the graph's grid) the value. Wait, actually, looking at the graph: 5am has 300 cars? Wait, no, the y - axis is number of cars, x - axis (vertical) is time? Wait, no, the graph: time is on the vertical axis (5am, 6am, 7am, 8am, 9am), and number of cars on the horizontal. Wait, maybe I misread. Wait, the graph: let's re - examine. The vertical axis (y - axis) is "Time" (5am, 6am, 7am, 8am, 9am) going down, and horizontal axis (x - axis) is "# of Cars". At 6:00 A.M. (time), the number of cars: let's see the point at 6am. The red line: at 5am, the number of cars is 300? Wait, no, maybe the x - axis is number of cars (300, 400, 500,...) and y - axis is time. So at 6:00 A.M. (y - axis), the x - value (number of cars) is 400? At 6:30 A.M., maybe the value is 500? Wait, no, the problem says "between 6:00 A.M. and 6:30 A.M.". Wait, maybe the graph: at 6:00 A.M., the number of cars is 400, and at 6:30 A.M., it's 500? Wait, no, let's check the grid. The horizontal axis: 300, 400, 500, 600, 700, 800, 900. The vertical axis: 5am, 6am, 7am, 8am, 9am. The red line: at 5am, it's at 300? Wait, no, the first point is at 5am with x = 300? Then at 6am, x = 400? At 7am, x = 600? At 8am, x = 800? At 9am, x = 700? Wait, maybe I got the axes reversed. Let's assume that the horizontal axis is number of cars, vertical is time. So to find the increase between 6:00 A.M. and 6:30 A.M., we need the number of cars at 6:00 and 6:30. Wait, maybe the time intervals: 6:00 - 6:30 is a half - hour. Let's look at the graph again. If at 6:00 A.M., the number of cars is 400, and at 6:30 A.M., it's 500? Wait, no, maybe the increase is 500 - 400 = 100? Wait, no, maybe the initial point at 5am is 300, at 6am is 400, at 7am is 600, at 8am is 800, at 9am is 700. Then between 6:00 (6am) and 6:30, the number of cars: let's see, the line from 6am (400 cars) to 7am (600 cars). So the time between 6am and 7am is 1 hour, divided into two half - hours (6:00 - 6:30 and 6:30 - 7:00). The increase from 400 to 600 in 1 hour, so per half - hour, the increase is 100. Wait, but maybe the graph is such that at 6:00 A.M., the number of cars is 400, and at 6:30 A.M., it's 500, so the increase is 500 - 400 = 100? Wait, the problem says "Type a whole number". Maybe the correct increase is 100? Wait, maybe I made a mistake. Let's start over.

Wait, the graph: the horizontal axis is the number of cars (300, 400, 500, 600, 700, 800, 900), vertical axis is time (5am, 6am, 7am, 8am, 9am). The red line: at 5am, x = 300; at 6am, x = 400; at 7am, x = 600; at 8am, x = 800; at 9am, x = 700. So between 6:00 A.M. (6am, x = 400) and 6:30 A.M. (half - way between 6am and 7am), the number of cars at 6:30 A.M. would be (400 + 600)/2 = 500? So the increase is 500 - 400 = 100.

Step2: Calculate the increase

Increase = Number of cars at 6:30 A.M. - Number of cars at 6:00 A.M. = 500 - 400 = 100.

To find during which half - hour the increase in the number of cars was the greatest, we calculate the increase for each option:

• Option A: 7:00 - 7:30. At 7:00 A.M. (7am), number of cars is 600; at 7:30 A.M., half - way to 8am (x = 800 at 8am), so number of cars at 7:30 is (600 + 800)/2 = 700. Increase = 700 - 600 = 100.
• Option B: 8:30 - 9:00. At 8:00 A.M., number of cars is 800; at 9:00 A.M., it's 700. This is a decrease, so increase is negative (we ignore, as we want increase).
• Option C: 6:00 - 6:30. As calculated before, increase is 100.
• Option D: 5:00 - 5:30. At 5:00 A.M., number of cars is 300; at 5:30 A.M., half - way to 6am (x = 400 at 6am), so number of cars at 5:30 is (300 + 400)/2 = 350. Increase = 350 - 300 = 50.

Wait, but wait, maybe the graph at 8:00 A.M. has 800 cars, and at 8:30 A.M., maybe it's 900? No, the graph at 9am is 700. Wait, maybe I reversed the time and cars. Wait, maybe the vertical axis is number of cars and horizontal is time. No, that doesn't make sense. Wait, another approach: the steeper the slope, the greater the increase. The slope between 7:00 - 8:00 A.M. (from 600 to 800 cars) is (800 - 600)/(1 hour)=200 cars per hour, so 100 cars per half - hour. Between 6:00 - 7:00 A.M.: from 400 to 600, slope is 200 cars per hour (100 per half - hour). Between 5:00 - 6:00 A.M.: from 300 to 400, slope is 100 cars per hour (50 per half - hour). Between 8:00 - 9:00 A.M.: from 800 to 700, slope is - 100 cars per hour (decrease). Wait, but the options are half - hour intervals:

• A. 7:00 - 7:30: part of 7:00 - 8:00 (slope 200 per hour, so 100 per half - hour)
• B. 8:30 - 9:00: part of 8:00 - 9:00 (slope - 100 per hour, decrease)
• C. 6:00 - 6:30: part of 6:00 - 7:00 (slope 200 per hour, 100 per half - hour)
• D. 5:00 - 5:30: part of 5:00 - 6:00 (slope 100 per hour, 50 per half - hour)

Wait, but maybe the graph at 7:00 - 8:00 has a steeper slope? Wait, no, 600 to 800 in 1 hour is 200, 400 to 600 in 1 hour is 200, 300 to 400 in 1 hour is 100, 800 to 700 in 1 hour is - 100. Wait, maybe the correct answer for part (b) is A? Wait, no, let's check the options again. Wait, the options are:

A. 7:00 - 7:30

B. 8:30 - 9:00

C. 6:00 - 6:30

D. 5:00 - 5:30

Wait, maybe I made a mistake in the slope. Let's look at the graph again. If at 7am, the number of cars is 600, at 8am it's 800, so the increase from 7am to 8am is 200 cars in 1 hour, so 100 cars in 30 minutes (7:00 - 7:30). At 6am, number of cars is 400, at 7am it's 600, so increase from 6am to 7am is 200 cars in 1 hour, so 100 cars in 30 minutes (6:00 - 6:30). At 5am, 300 cars, at 6am 400 cars, increase of 100 cars in 1 hour, so 50 cars in 30 minutes (5:00 - 5:30). At 8am, 800 cars, at 9am 700 cars, decrease of 100 cars in 1 hour, so decrease in 30 minutes (8:30 - 9:00). Wait, but then both A and C have an increase of 100? But that can't be. Wait, maybe the graph at 7:00 - 8:00 has a steeper slope? No, 600 to 800 is 200 in 1 hour, 400 to 600 is 200 in 1 hour. Wait, maybe the initial point at 5am is 300, at 6am is 400, at 7am is 600, at 8am is 800, at 9am is 700. So the intervals:

• 5:00 - 5:30: from 300 to (300 + 400)/2 = 350, increase 50.

• 5:30 - 6:00: from 350 to 400, increase 50.

• 6:00 - 6:30: from 400 to (400 + 600)/2 = 500, increase 100.

• 6:30 - 7:00: from 500 to 600, increase 100.

• 7:00 - 7:30: from 600 to (600 + 800)/2 = 700, increase 100.

• 7:30 - 8:00: from 700 to 800, increase 100.

• 8:00 - 8:30: from 800 to (800 + 700)/2 = 750, decrease 50.

• 8:30 - 9:00: from 750 to 700, decrease 50.

Wait, but the options are A. 7:00 - 7:30, B. 8:30 - 9…

Answer:

(part a):
100

Part (b)