### Home > GB8I > Chapter 9 Unit 10 > Lesson INT1: 9.3.2 > Problem9-86

9-86.

During a race, Bernie ran $9$ meters every $4$ seconds, while Wendel ran $2$ meters every second and got a $9$-meter head start. If the race was $70$ meters long, did Bernie ever catch up with Wendel? If so, when? Justify your answer.

Define variables and write an equation for Bernie and an equation for Wendel.
$x =$ time in seconds
$y =$ distance in meters

$\text{Bernies's rate} = \frac{9\text{ meters}}{4\text{ seconds}}$

$\text{Wendel's rate} = \frac{2\text{ meters}}{1\text{ second}}$     $9 \text{ meter headstart = starting point}$

$y=\frac{9}{4}x$

$y = 2x + 9$

To catch up, their equations would need to be equal.

$\frac{9}{4}x=2x+9$

$y = 81$ meters, remember to substitute $x$ back into one of the original equations to solve for $y$.
Bernie can't catch up with Wendel in $70$ meters.

Use the eTool below to graph the equations for Bernie and Wendel.
Look at your graph to determine if Bernie ever caught up with Wendel and if so, when.
Click on the link at right for the full eTool version: 9-86 HW eTool