Let H represent the height of the individuals in rungs and t represent the time in seconds that
passes while they climb.
.
Bob starts at rung 30 and goes down at a rate of -2 rungs per second. So the equation for
Bob's height is:
.
H = -2*t + 30
.
Meanwhile, Rob starts at rung 0 and goes up at a rate of +1 rung per second. So the equation
for Rob's height is:
.
H = t + 0 = t
.
You are interested in finding the height (in rungs) where the two will be standing on
the same rung. Since the two heights are the same, we can set the right sides of our two
height equations equal. So we can say that:
.
-2*t + 30 = t
.
To solve this equation for t, first get rid of the 30 on the left side by subtracting
30 from both sides of the equation. This subtraction converts the equation to:
.
-2*t = t - 30
.
Next get rid of the t on the right side by subtracting t from both sides. The equation then
becomes:
.
-3*t = -30
.
Solve for t by dividing both sides of this equation by -3 to find that:
.
t = -30/-3 = 10 seconds
.
In 10 seconds Rob will have climbed to rung number 10 because he climbs at 1 rung per
second. And in 10 seconds at a rate of 2 rungs per second Bob will climb down 20 rungs. But
Bob started on rung 30 so he will be at rung 10 also because 30 - 20 = 10.
.
Hope this helps you to understand the problem a little better.
