Meaning: mutual cooperation can help both parties.
It is similar to other proverbs, like "one good turn deserves another" and "you
scratch my back and I'll scrtach yours."
- www.phrases.org.uk
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I first heard this in Malcolm X, the 1992 movie which I watched dozens of times.
Malcolm, after helping growing the Nation of Islam from 500 to 30,000 members
over ten years, found out about its leader(Elijah Muhammad)'s affairs. Crushed,
he turned to Brother Baines, an old comrade from their prison days and a senior
member of the Nation, who explained:
"Now, about our coming up in the world a little. The Nation's grown. We've
grown with it. You know our people. They want their leaders to be
prosperous. One hand washes the other."
and later
"Do you know your Bible? David slept with Bathsheba, but he's remembered for
slaying Goliath. Noah was accused of drunkenness, but God gave him the ark.
Solomon had 700 wives but he was the greatest, wisest king in history."
and
"The great man's deeds outweigh his personal weaknesses."
The scripts come mostly from "The Autobiography of Malcolm X," an enlightening
read.