Let s=speed of the car on an interrupted journey. The time, t for the journey=80/s hours.
But t-24/60 hrs is the time she has left to do the journey at a speed of s+10, so t-0.4=80/(s+10).
Therefore 80/s-0.4=80/(s+10).
Multiply through by s(s+10): 80(s+10)-0.4s(s+10)=80s.
80s+800-0.4s^2-4s=80s, 0.4s^2+4s-800=0,
s^2+10s-2000=0=(s-40)(s+50) and s=40 kph.
Let's check. Time for uninterrupted journey=80/40=2 hrs.
Time for interrupted=80/50=1.6 hrs=1hr 36min, which is 24 mins short of 2 hours. So the time for the interrupted journey including the stop at the coffee shop is 1hr 36mins + 24 mins=2 hours.
Speed of the car was 40km/hr.