I think it is meant like this:
Yes exactly.
Missile Mach 3= 3675km/h lets round it down to 3600
Target Mach 2=2450km/h lets round it down to 2400
Let's say a Turkish F-16 detects an enemy fighter 100km away and fires a Gokhan missile while both targets fly at Mach 0,9. Let's assume for simplicity both the missile and target instantly reach Mach 2 and Mach 3 and both the missile and the target follow a linear path.
The missile will travel 1 km per second.
The fighter travels 0,6666667km per second.
The missile closes the distance by 0,3333333km per second.
The missile will catch the target after ~300 seconds.
The missile will travel 300km in 300 seconds. If your missile has a range lower than 300km it will miss its target.
And now let's assume that our missile flies at Mach 4 (4900km/h lets round down it to 4800 for the sake of simplicity)
Our missile travel 1,3333km per second
The fighter is the same
The missile closes the distance by 0,666666663km per second
The missile will catch the target after ~150 seconds
The missile will travel ~200km in ~150 seconds. If our missile has a range greater than 200km it will hit its target.
So you can shave off 100km or 1/3 range when you go from Mach 3 to Mach 4. So let's assume fuel consumption is increased by %33 for the second missile. In this case, both of the missiles will carry a similar amount of fuel. At any ratio of more than %33, the second missile has to carry more fuel compared to the first one if the fuel composition is the same. The second missile has the advantage of shorter flight time which is also important. If somehow you made a breakthrough that enables a more efficient fuel burn(lower than %33 increase at Mach 4) with the same fuel or formulated a better fuel. You can design a more compact missile.
There are trade-offs. It is not a simple linear comparison you burn more fuel at Mach 4 less at Mach 3.
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