It is not necesssary to know the distance to solve this problem. We have two equations:
D = S * T walking at normal speed, any chosen distance takes T time
D = 0.75S * (T + 10) walking at 3/4 speed, any chosen distance takes T time plus 10 minutes
Because the distance is the same in both equations, the equations are equal to each other:
ST = 0.75S * (T + 10) = 0.75 * ST + 7.5 * S
Subtract 0.75 *ST from both sides of the equation
0.25 ST = 7.5 S
Divide both sides by S
0.25 T = 7.5
Multiply both sides by 4
T = 30 minutes
Choose any walking speed withing reason, e.g., 4 miles per hour
D = 4mph * 0.5hr = 2 miles
D = (0.75 * 4mph) * (2/3 hr) < 30 minutes + 10 minutes = 40 minutes or 2/3 hr
D = 3mph * 2/3 hr = 2 miles
Both equations give the same distance.
How about walking at 6mph? Fast, but for demo purposes....
D = 6mph * 0.5hr = 3 miles
D = (0.75 * 6mph) * (2/3 hr)
D = 4.5mph * 2/3 hr = 3 miles
Therefore, his usual time is 30 minutes.