Time for two bodies to collide under mutual gravity

[the-genius]

Homework Statement

There Are two bodies with mases M1 and M2 placed in space separated by a distance D. They attract each other due to gravitational forces and hence acclerate towards each other.The problem is to Find out the time taken before their collision?

Homework Equations

I know that, the acceleration is provided by the gravitational force so,
a=G*M/x^2 for each body where M is the other body's mass and x is the distance from other body at that instant.

The Attempt at a Solution

I am hopless at attemting a solution.
Had my equation of accelartion, dependent on time (like a = Kt^2 + Ct ... etc) I could integrate with respect to time and find instanteneus velocity with respect to time. Then I could Integrate V.dt for a certain time to get distance, and etc. But here acceleration varies with distance,
I tried to convert dt to dx but failed.
So, please Help

 

[LowlyPion]

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