Troubleshooting a Uniform Acceleration Problem: Finding Time and Height

[Delber]

I'm having trouble with this problem. I can't seem to wrap my head around it and any help would be appreciated.

Homework Statement

The problem is:
A stone falls from the top of the cliff. One second later, another falls from a ledge 45m below the top. The two stones hit the bottom simultaneously. Find the time taken for the first stone to fall and the height of the cliff.

Homework Equations

x = ut+ 1/2at^2 where x is distance and u is initial velocity

The Attempt at a Solution

I tried a couple attempts at the problem. I began by trying to make two equations equal together, but I ran into the problem that the time and distance traveled is not equal so I tried to make a system of equations. I can't figure out how to make a suitable system where I can easily solve for one variable.

 

[_Mayday_]

Delber, I would first split the two stones into two different things. For the second stone what do you have infromation on? You have x, u and a so surely you can work out the time for the second stone? With that value for time you can calculate the time for the first stone, and again see what values you have.

With these questions usually all the infomration is given and it is a case of writing down what you are told and then seeing what formula works with them.

Have another go

 

[Delber]

Sorry, but I do not see how I have x to solve for the time of the second stone. The distance traveled of the second stone is only given as an measurement from where the first stone dropped off the cliff.