A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.

The number of minutes m that Nick will spend washing his car given that he has $10 will be:

Cost for spending 5 min is $4, any additional minutes will be $0.75 per minutes.

amount of cash Nick will remain with after spending $4 will be:

10-4=$6

the total extra minutes he will spend will be:

6=0.75*m

0.75m=6

thus

m=6/0.75

m=8 min

the total number of minutes that Nick will spend with $10 will be:

8+5=13 min