Songwriting Sessions: Inspired by Other Musicians

When I was a kid there was a song I used to hear on the radio that I really enjoyed. The song was called "Running Up That Hill" by Kate Bush. Here it is on youTube:

As an adult I've been loving Coldplay pretty much since I've known of their existence. I was particularly excited when they released their album X & Y, which featured many great songs. Here's one of them, "Speed of Sound":

Notice any similarities between these two songs? Listen in particular to the chorus of both songs (the "If I only could/I'd make a deal with God" in "Running Up That Hill" vs "All that noise/All that sound" in "Speed of Sound")

It's not really obvious (at least it wasn't to me), but "Running Up That Hill" was the direct inspiration for "Speed of Sound". If nothing else, this proves to me that you can write a great song based on someone else's great song, without the two songs sounding too similar.