We have a car which has cruise control which can be set to a whole number of miles per hour. It can also inform you what your average speed was over a given journey.

My wife drove to her mother's house about 2 weeks ago, she texted me when she got there ands said: "I got here by driving at just 2 different speeds on the cruise control, and the average speed the car displayed was a whole number of miles per hour equal to the sum of the two speeds divided by two."

After her return along the same route she said: "for my return journey I used the same two speeds as before but I had to add a third cruise speed to go through some roadworks, which was lower than the other two. My average speed was a whole number of miles per hour again, equal to the sum of the three speeds, divided by three.".

What are the minimum, and the maximum time (in whole minutes) that her return journey might have taken? (ignore acceleration and deceleration)

My wife drove to her mother's house about 2 weeks ago, she texted me when she got there ands said: "I got here by driving at just 2 different speeds on the cruise control, and the average speed the car displayed was a whole number of miles per hour equal to the sum of the two speeds divided by two."

After her return along the same route she said: "for my return journey I used the same two speeds as before but I had to add a third cruise speed to go through some roadworks, which was lower than the other two. My average speed was a whole number of miles per hour again, equal to the sum of the three speeds, divided by three.".

What are the minimum, and the maximum time (in whole minutes) that her return journey might have taken? (ignore acceleration and deceleration)