Question

Please help me with this graph problem. NO LINKS!!! ​

Answer 1

Part (a)

Given:

• Average running speed = 200 m/min
• Average walking speed = 80 m/min

If 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 walking
• 6 minutes running, 5 minutes walking

Answer 2

Explanation:

a)

Eric runs for 4 min and walks for 8 min.

The distance covered is

• 4*200 + 8*80 = 800 + 640 = 1440

The goal of 1600 m is not met, needs additional 160 m

b)

The equation of distance is

• d = 200x + 80y

c)

For d = 1600, the equation is

• 200x + 80y = 1600

Simplified form of it

• 2.5x + y = 20

Some combinations of x and y to make the equation right

• x = 2, y = 15
• x = 4, y = 10
• x = 6, y = 5

d)

See the attached graph for more combinations, where the first coordinate represents running time and the second coordinate - walking time