Final answer:
The distance traveled on foot by the man can be found by setting up two equations based on distance (x + y = 61 km) and time (x/4 + y/9 = 9 hours), then solving the system to find x.
Step-by-step explanation:
To solve for the distance traveled on foot by the man, let's set up a system of equations based on the given information. We know that the total distance traveled is 61 km, and it was done in two parts: on foot and on a bicycle.
Let the distance traveled on foot be x km at a rate of 4 km/hr, and the distance traveled on a bicycle be y km at a rate of 9 km/hr. The total time spent on the journey is 9 hours. Based on this, we can set up two equations: Equation for distance: x + y = 61 km, Equation for time: x/4 + y/9 = 9 hours
To find x, solve the system of equations. Multiplying the second equation by 36 (the least common multiple of 4 and 9) to eliminate the fractions, we get: 9x + 4y = 324. Now use the substitution method or any other relevant method to find the value of x, which represents the distance traveled on foot.