### Learning Math and Coding with Robots

 Grid: Tics Lines: Width px Hash Lines: Width px Labels: Font px Trace Lines: Robot 1: Width px Robot 2: Width px Robot 3: Width px Robot 4: Width px
 Axes: x-axis y-axis Show Grid Grid: 24x24 inches 36x36 inches 72x72 inches 96x96 inches 192x192 inches Quad: 4 quadrants 1 quadrant Hardware Units: US Customary Metric
 Background:

#### Robot 1

 Initial Position: ( in, in) Initial Angle: deg Current Position: (0 in, 0 in) Current Angle: 90 deg Wheel Radius: 1.75 in1.625 in2.0 in Track Width: in

#### Robot 2

 Initial Position: ( in, in) Initial Angle: deg Current Position: (12 in, 0 in) Current Angle: 90 deg Wheel Radius: 1.75 in1.625 in2.0 in Track Width: in

#### Robot 3

 Initial Position: ( in, in) Initial Angle: deg Current Position: (24 in, 0 in) Current Angle: 90 deg Wheel Radius: 1.75 in1.625 in2.0 in Track Width: in

#### Robot 4

 Initial Position: ( in, in) Initial Angle: deg Current Position: (36 in, 0 in) Current Angle: 90 deg Wheel Radius: 1.75 in1.625 in2.0 in Track Width: in

Use Proportions to Animate an Hourglass
Problem Statement:
The pre-placed blocks animate the sand decreasing from the top of the hourglass. If the ratio of the rate of sand decreasing on the top to the rate of sand increasing on the bottom is 4:1, write an expression in terms of i for the variable yBot to increase the sand on the bottom at the correct rate.
```/* Code generated by RoboBlockly v2.0 */
#include <chplot.h>
double i;
double y;
double x;
double x2;
double yBot;
double xBot1;
double xBot2;
CPlot plot;

for(i = 1; i <= 18; i += 0.25) {
plot.strokeColor("black");
plot.fillColor("#ccffff");
plot.triangle(0, 0, 18, -34, -18, -34);
plot.triangle(0, 0, 18, 34, -18, 34);
plot.noStrokeColor();
plot.fillColor("#996633");
y = 18 - i;
x = (0.592 - 0.05) * y;
x2 = (-0.592 + 0.05) * y;
plot.triangle(x, y, 0, 0, x2, y);
yBot = -34 + i * 0.25;
xBot1 = (0.592 - 0.05) * yBot;
xBot2 = (-0.592 + 0.05) * yBot;
plot.quad(-18, -34, 18, -34, xBot2, yBot, xBot1, yBot);
delaySeconds(0.03);
}

plot.label(PLOT_AXIS_XY, "");
plot.grid(PLOT_OFF);
plot.tics(PLOT_AXIS_XY, PLOT_OFF);
plot.axis(PLOT_AXIS_XY, PLOT_OFF);
plot.axisRange(PLOT_AXIS_XY, -48, 48);
plot.ticsRange(PLOT_AXIS_XY, 12);
plot.sizeRatio(1);
plot.plotting();```
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Problem Statement:
The pre-placed blocks animate the sand decreasing from the top of the hourglass. If the ratio of the rate of sand decreasing on the top to the rate of sand increasing on the bottom is 4:1, write an expression in terms of i for the variable yBot to increase the sand on the bottom at the correct rate.

Time