Answers
Step-by-step explanation:
a)
Eric runs for 4 min and walks for 8 min.
The distance covered is
4*200 + 8*80 = 800 + 640 = 1440The goal of 1600 m is not met, needs additional 160 m
b)
The equation of distance is
d = 200x + 80yc)
For d = 1600, the equation is
200x + 80y = 1600Simplified form of it
2.5x + y = 20Some combinations of x and y to make the equation right
x = 2, y = 15x = 4, y = 10x = 6, y = 5d)
See the attached graph for more combinations, where the first coordinate represents running time and the second coordinate - walking time
Answer:
Part (a)Given:
Average running speed = 200 m/minAverage walking speed = 80 m/minIf Eric runs for 4 minutes ⇒ 200 x 4 = 800 m
If Eric walks for 8 minutes ⇒ 80 x 8 = 640 m
Total distance covered = 800 + 640 = 1440 m
Therefore, he is 160 m away from his 1600 m goal.
Part (b)Let x = number of minutes Eric runs
Let y = number of minutes Eric walks
Let d = total distance Eric covers
Equation: d = 200x + 80y
Part (c)Set d = 1600, then rewrite to make y the subject:
200x + 80y = 1600
⇒ 5x + 2y = 40
⇒ 2y = 40 - 5x
⇒ y = 20 - 2.5x
Now find ordered pairs (points on the line):
x-intercept (y = 0): 20 - 2.5x = 0 ⇒ x = 8 ⇒ (8, 0)y-intercept (x = 0): 20 - 2.5(0) = 20 ⇒ (0, 20)when x = 4: 20 - 2.5(4) = 10 ⇒ (4, 10)Part (d)Plot (8, 0) (0, 20) and (4, 10) and connect with a straight line.
(see attached graph)
From inspection of the graph, other combinations of running and walking times for which Eric would cover 1600 meters are:
2 minutes running, 15 minutes walking6 minutes running, 5 minutes walking
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