Question

NO LINKS!! You have 4 contestants in the second heat of the big race:
The equations for the contestants are:
1. Mr. Pace: y= 3/4x + 4
2. Mr. Glintz: y= 2/3x + 7
3. Ms. Liskey: y= 3x
4. Mr. Brininger: y= 1/2x + 10

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Answer 1

Answer:

Part (c):

• 1st Place:  Ms. Liskey
• 2nd Place:  Mr. Glintz
• 3rd Place:  Mr. Pace
• 4th Place:  Mr. Brininger

Part (d):

• 1st Pass:     Mr Pace           Time:  1.78 s (2 d.p.)
• 2nd Pass:   Mr Glintz          Time:  3 s
• 3rd Pass:    Mr Brininger    Time: 4 s

Part (e):

• y = 3x + 2

Step-by-step explanation:

Given equations:

$\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4$

$\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7$

$\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x$

$\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10$

Plot the lines on the given coordinate plane.

(See attachment).

Draw a line at y = 25 to represent the distance at the finish line.

Find the points of intersection of the linear equation of each contestant and the finish line equation y =25.  The point with the smallest x-value is the contestant who is first place.

Mr Pace

$\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}$

Mr Glintz

$\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}$

Mr Liskey

$\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}$

Mr Brininger

$\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}$

Therefore, the order in which the contestants reached the finish line is:

• 1st Place:  Ms. Liskey
• 2nd Place:  Mr. Glintz
• 3rd Place:  Mr. Pace
• 4th Place:  Mr. Brininger

From inspection of the attached graph, Ms Liskey (red line) passes all three contestants.  To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.

Mr Pace

$\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}$

Mr Glintz

$\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}$

Mr Brininger

$\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}$

Therefore:

• 1st Pass:  Mr Pace            Time:  1.78 s (2 d.p.)
• 2nd Pass:  Mr Glintz         Time:  3 s
• 3rd Pass:  Mr Brininger    Time: 4 s

If you want to win the race, either:

• increase the slope of Ms Liskey's equation:  y = 4x
• or add a value to Ms Liskey's equation:  y = 3x + 2