Question

Please help with this problem, my test's tomorrow and i dont know how to solve it. You have to use 1 or 2 equations, that's all i know.
Bob climbed down a ladder from his roof, while Roy climbed up another ladder next to him. Each ladder had 30 rungs. Their friend Jill recorded the following information about Bob and Roy:
Bob went down 2 rungs every second.
Roy went up 1 rung every second.
At some point, Bob and Roy were at the same height. Which rung were they on?

Answer 1

Lets use "B" to stand for Bob and 'R' to stand for Roy. Call the ground Run Zero and the top Rung 30.

At time zero we know that Bob is at the top of his ladder i.e. B=30. We also know that at this same time Roy is at the bottom of his ladder i.e.: R=0 So far:\[B=30\]and\[R=0\]when\[t=0\].

We know that Bob goes down two rungs per second\[B=30-2t\] and Roy goes up 1 per second\[R=0+1t\].

We want to find when these are equal \[B=R\]\[30-2t=t\]\[30=3t\]\[t=10\]

We can now find the rungs for each:

Bob:
\[B=30-2(10)=10\]
Roy:\[R=t=10\]

They will cross after 10 seconds when both are on rung 10.

Answer 2

thank you!!