answer and solution both are correct
I think you are confusing the unit of measure minute.
If you take minute to be the unit of time then the first result holds wherein 1 degree = 4 minute.
This is easy to calculate too:
There are 24 hours in one day and 60 minutes in one hour, equalling 24*60 = 1440 minutes in a day.
Now, you may know the fact that Earth has different timezones depending on the longitude that they lie on. These are measured starting from the Greenwich meridian and extend to +180° and -180° in the two directions of East and West respectively. This totals to 360°.
Now to calculate the time difference between two longitude separated by 1° is done by dividing the total number of minutes in a day, by the total angle covered in a day. i. e.
1440/360 = 4 minutes.
Now for the other minute.
The angular measure of degree can be sub divided into smaller parts known as minute, and the relationship that holds is:
1° = 60' = 60 minutes.
Another thing that can be derived from this is:
1° = 60 minutes(') = 4 minutes.
i. e. 15 minutes(') = 1 minute.