Question

Two hikers are 33 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 4.4 mph faster than the other.

Answer 1

slower hiker's speed = 1.1 mph

faster hiker's speed = 5.5 mph

Explanation:

Extracting the key information from the question:

*** Two hikers are 33 miles apart and are walking towards each other.

*** One of them walks 4.4 mph faster than the other and later met themselves in 5 hours.

*** We are required to find the speed of each of the hikers.

Speed = distance/time

Let us use "x" to represent the slower speed. Since one of the hikers was 4.4 mph faster than the other hiker, we can represent the faster speed with x+4. Now, if they met themselves in 5 hours, even though they were 33 miles apart initially, then we can represent the situation with the given equation:-

(x mph × 5hours) + [(x+4.4)×5] = 33 miles

5x + (5x + 22) = 33

5x + 5x + 22= 33

10x + 22 = 33

10x = 33-22

10x = 11

x = 11/10

x = 1.1mph (speed of slower hiker)

The speed of the faster hiker = x + 4.4

= 1.1 + 4.5

= 5.5mph

Answer 2

slow hiker rate= 1.1mph and fast hiker rate= 5.5 mph

Explanation:

lets consider the Speed of the slow hiker =x

Then Speed of fast hiker =x+4.4

As we know that distance is the product of speed and time

therefore,

Distance covered by slow hiker in 5 hours = 5x km

Distance covered by fast hiker in 5 hours=5 (x+4.4)=5x+22 km

As they are are 33 miles apart , therefore

5x + 5x+22 = 33

10x = 33-22

10x = 11

x =11/10 => 1.1

Rate of slow hiker is x i.e 1.1mph

Rate of fast hiker = x+4.4 => 5.5 mph