Two hikers are 22
miles apart and walking toward each other. They meet in 5
hours. Find the rate of each hiker if one hiker walks 2.2
mph faster than the other.
Let's denote the rate of the slower hiker as x mph.
Since the other hiker walks 2.2 mph faster, the rate of the faster hiker is x + 2.2 mph.
When they walk toward each other, their combined rate is the sum of their individual rates:
x + (x + 2.2) = 2x + 2.2
We know that distance = rate × time. In this case, the distance is 22 miles, and the time is 5 hours. So we can set up the equation:
22 = (2x + 2.2) × 5
Simplifying the equation:
22 = 10x + 11
Rearranging the equation:
10x = 22 - 11
10x = 11
x = 11/10
x = 1.1
Therefore, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 1.1 + 2.2 = 3.3 mph.
To find the rate of each hiker, we can set up a system of equations based on the given information.
Let's assume that the rate of the slower hiker is represented by x mph. Since the other hiker is walking 2.2 mph faster, the rate of the faster hiker can be represented as (x + 2.2) mph.
We know that the hikers are 22 miles apart and will meet in 5 hours. Since they are walking toward each other, their combined distance traveled is equal to the total distance between them.
The equation for the distance traveled by the slower hiker can be expressed as:
Distance = Rate × Time
Distance = x mph × 5 hours
Distance = 5x miles
Similarly, the equation for the distance traveled by the faster hiker can be expressed as:
Distance = Rate × Time
Distance = (x + 2.2) mph × 5 hours
Distance = 5(x + 2.2) miles
Since their combined distance is 22 miles, we can add the distances traveled by the slower and faster hiker together:
5x + 5(x + 2.2) = 22
Expanding and simplifying the equation:
5x + 5x + 11 = 22
10x + 11 = 22
10x = 11
x = 1.1
So, the rate of the slower hiker is 1.1 mph. To find the rate of the faster hiker, we can substitute this value back into the equation x + 2.2:
Rate of faster hiker = x + 2.2
Rate of faster hiker = 1.1 + 2.2
Rate of faster hiker = 3.3 mph
Therefore, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 3.3 mph.
1st hiker walks X mi/h.
2nd hiker walks (x+2.2) mi/h.
d1 + d2 = 22 miles.
sx + 5(x+2.2) = 22. X = ?.