Final answer:
To solve the speed problem, we establish two equations based on distance-speed-time relationships setting Jill's speed as x and Katie's as x + 10. Solving the equations reveals that Jill walks at 5 km/h and Katie bikes at 15 km/h.
Step-by-step explanation:
The problem given is a classic example of a distance-speed-time question, commonly found in mathematics, particularly in algebra-related topics. To solve this problem, we need to establish the relationship between the speeds of Katie and Jill, and how these relate to the distances they travel in the given times.
Let's define the speed at which Jill walks as 'x' km/h. Since Katie rides her bike at a speed 10 km/h faster than Jill walks, we can define Katie's speed as 'x + 10' km/h. We know that distance equals speed multiplied by time, and since they both travel the same distance, we can set up the following equation based on the relation distance (d) = speed (v) × time (t):
- Jill's distance: d = x × 3 hours
- Katie's distance: d = (x + 10) × 1 hour
Since these distances are equal, we can equate them to solve for 'x':
3x = x + 10
By simplifying this equation, we get:
2x = 10
x = 5
So, Jill walks at a speed of 5 km/h, and Katie rides her bike at a speed of 5 + 10 = 15 km/h. Checking if the answer is reasonable, it seems plausible since within an hour, Katie would travel three times the distance Jill covers in three hours.