How do I solve this problem?

Question

When Fritz drives to work his trip takes 48 minutes, but when he takes the train it takes 40 minutes. Find the distance Fritz travels to work if the train travels an average of 6 miles per hour faster than his driving.

Answer 1

48 min = 48/60 = 4/5 hr

40 min = 40/60 = 2/3 hr

Distance = rate * time

= r * (4/5)

= (r+6)*(2/3)

(4/5)r = (2/3)(r+6)

(4/5)r = (2/3)r + 4

12r = 10r + 60

2r = 60

r = 30

Distance = (4/5)(30) = 24 miles

= (2/3)(36) = 24 miles

24 miles = (2/3) hours * 36 mph

= (4/5) hr * 30 mph

24 miles (2/3) hours at 36 mph

(4/5) hours at 30 mph

24 miles