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(a)
The distance at which the Team C’s runner passed Team B’s runner.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 30E
It seems that distance at which Team C’s runner passed Team B‘s runner is 40 meters.
Explanation of Solution
Given information:
Formula used:
The x-axis represents the time in seconds and the y axis represents distance in meters.
Calculation:
From the graph, it seems that distance at which Team C’s runner passed Team B‘s runner is 40 meters.
Conclusion:
It seems that distance at which Team C’s runner passed Team B‘s runner is 40 meters.
(b)
The races are longer than Team C’s runner have passed Team A’s runner.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 30E
For a longer race, Team C’s runner could have passed Team A’s runner.
Explanation of Solution
Given information:
Formula used:
The x-axis represents the time in seconds and the y axis represents distance in meters.
Calculation:
Since, the slopes of line corresponding to Team A and Team C are different, the two lines would intersect at some point and that happens for t > 0. At this point, Team C’s runner would have passed Team A’s runner.
In graph we can see that that it would happen for distance greater than 200 meters. Thus, for a longer race, Team C’s runner could have passed Team A’s runner.
Conclusion:
For a longer race, Team C’s runner could have passed Team A’s runner.
(c)
The race being longer Team B’s runner have passed Team A’s runner.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 30E
Even in a longer race, Team B’s runner cannot pass Team A’s runner.
Explanation of Solution
Given information:
Formula used:
The x-axis represents the time in seconds and the y axis represents distance in meters.
Calculation:
Since, the slope of lines corresponding to Team A and Team are same but intercepts are different. The two lines never intersect. This means that Team A would always be ahead of Team B.
Thus, even in a longer race, Team B’s runner cannot pass Team A’s runner.
Conclusion:
Even in a longer race, Team B’s runner cannot pass Team A’s runner.
Chapter 5 Solutions
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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