Aself-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