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Unstable traffic flow occurs when drivers accelerate and brake too often, wasting energy. The table below gives one example of traffic speeds, in kilometers per hour (km/h), in an unstable flow situation.

| Time (p.m.) | 4:00 | 4:10 | 4:20 | 4:30 | 4:40 | 4:50 | 5:00 |
|-------------|------|------|------|------|------|------|------|
| Speed (km/h)| 30 | 20 | 50 | 70 | 20 | 70 | 20 |

What is the mean speed, in km/h, in this situation? You may use a calculator.

A. 20
B. 30
C. 40
D. 50



Answer :

GinnyAnswer
To find the mean speed, we need to calculate the average of the given speeds at different times. Here are the speeds given:

- At 4:00 p.m. the speed was 30 km/h
- At 4:10 p.m. the speed was 20 km/h
- At 4:20 p.m. the speed was 50 km/h
- At 4:30 p.m. the speed was 70 km/h
- At 4:40 p.m. the speed was 20 km/h
- At 4:50 p.m. the speed was 70 km/h
- At 5:00 p.m. the speed was 20 km/h

First, we sum up all these speeds:

[tex]\[ 30 + 20 + 50 + 70 + 20 + 70 + 20 \][/tex]

Adding these values together:

[tex]\[ 30 + 20 = 50 \][/tex]
[tex]\[ 50 + 50 = 100 \][/tex]
[tex]\[ 100 + 70 = 170 \][/tex]
[tex]\[ 170 + 20 = 190 \][/tex]
[tex]\[ 190 + 70 = 260 \][/tex]
[tex]\[ 260 + 20 = 280 \][/tex]

So, the total sum of speeds is 280 km/h.

Next, we count the number of time intervals given. There are 7 intervals.

To find the mean speed, we divide the total sum of speeds by the number of intervals:

[tex]\[ \text{Mean Speed} = \frac{280}{7} = 40 \text{ km/h} \][/tex]

Thus, the mean speed in this unstable traffic flow situation is [tex]\(\boxed{40}\)[/tex] km/h.

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