First work out your groundspeed. Lacking a nav computer I will do it by calculation:
Temperature in Kelvin = 273 – 38 = 235K
Local speed of sound = 38.94*sqrt 235 = 597KT
TAS = Mach number * LSS = 472KT
Groundspeed = 472KT – 70KT = 402KT
At 07:33 you were 500NM from Z. You are required to reduce speed to 320KT groundspeed to cross at 08:57.
Consider where you would be at 08:57 if you did not change speed. You would have travelled for 1 hr 24 minutes (1.4 hours) at 402KT, a distance of:
1.4 * 402 = 562NM, an ‘overshoot’ of 62NM.
You need to get rid of this overshoot by flying 402 – 320 = 82KT slower.
This will take 63 ÷ 82 = 0.77 hours = 46 minutes.
Therefore change speed 46 minutes before 08:57, or 08:11.
I have rounded numbers here but preserved decimal places on my calculator to actually get 45.8 minutes. How did I do?