Question

In Exercise 3, one equation relating the times Eric spends running and walking to reach the goal of covering 1600 meters is 200x + 80y=1600. Suppose Eric runs and walks for a total of 12 minutes to reach his goal.

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Answer 1

Given equation:

`200x+80y=1600`

where:

• x = time Eric runs (in mins)
• y = time Eric walks (in mins)

Part (a)

If Eric runs and walks for a total of 12 minutes, then:

`x+y=12`

Part (b)

To graph:

• Rewrite both equations to make y the subject
• Find the x-intercept
• Find the y-intercept
• Connect the two points with a straight line

`200x+80y=1600 \implies y=20-(5)/(2)x`

`\textsf{x-intercept}: \quad 20-(5)/(2)x=0 \implies x=8 \implies (8,0)`

`\textsf{y-intercept}: \quad 20-(5)/(2)(0)=20 \implies (0,20)`

`x+y=12 \implies y=12-x`

`\textsf{x-intercept}: \quad 12-x=0 \implies x=12 \implies (12,0)`

`\textsf{y-intercept}: \quad 12-0=12 \implies (0,12)`

Point of intersection (equate equations):

`\begin{aligned}20-(5)/(2)x &=12-x\\20-12 &=(5)/(2)x-x\\8&=(3)/(2)x\\16 &=3x\\x &=(16)/(3)\end{aligned}`

`y=12-(16)/(3)=(20)/(3)`

`\implies \left((16)/(3),(20)/(3)\right)`

The point of intersection tells us that Eric runs for 16/3 mins and walks for 20/3 minutes.

Answer 2

Answer + Step-by-step explanation:

let x be the time that Eric spends running

y be the time that Eric spends walking

a) the statement “Eric runs and walks for a total of 12 minutes to reach his goal” is equivalent to the equation: x + y = 12

b) the coordinates of the intersection point are (5.333... , 6.666...)

Interpretation:

the time that Eric spends running is 5.333... minutes

the time that Eric spends walking is 6.666... minutes