How does a read-write mutex/lock work?

Let's say I'm programming in a threading framework that does not have multiple-reader/single-writer mutexes. Can I implement their functionality with the following:

Create two mutexes: a recursive (lock counting) one for readers and a binary one for the writer.

Write:

• acquire lock on binary mutex
• wait until recursive mutex has lock count zero
• actual write
• release lock on binary mutex

Read:

• acquire lock on binary mutex (so I know the writer is not active)
• increment count of recursive mutex
• release lock on binary mutex
• actual read
• decrement count of recursive mutex

This is not homework. I have no formal training in concurrent programming, and am trying to grasp the issues. If someone can point out a flaw, spell out the invariants or provide a better algorithm, I'd be very pleased. A good reference, either online or on dead trees, would also be appreciated.