Mackenzie drives to work at 50 mph and arrives 1 min late. She drives to work at 60 mph and arrives 5 min early. How far does Mackenzie live from work?

What we know:

The difference in time between driving 50mph vs 60mph is 6 minutes (1minute late vs 5minutes early)

Equations:

t1(x)=(60minutes/50miles)*x

t2(x)=(1min/1mile)*x

t1(x)-t2(x)=6

Solve:

(6/5)x-x=6

(6/5)x-(5/5)x=6

(1/5)x=6

x=30miles

Check:

30miles * (60minutes/50miles) = 36minutes

30miles * (1minute/1 mile) = 30 minutes