Distance Problem - Solving for Rate

Question

Two hikers are 12 miles apart and walking toward each other. They meet in

2 hours. Find the rate of each hiker if one hiker walks 1.2 mph faster than the other.

How do you get the difference of the rates?

Answer 1

First, define your variables. To keep things simple, I'll define my variables this way:

x = the rate of the first hiker

y = the rate of the second hiker

d = the distance closed between the hikers

t = the time it takes for the hikers to meet

The problem tells you that initially, the hikers are 12 miles apart, one hiker walks 1.2 mph faster than the other, and it takes 2 hours for them to meet. So,

d = 12 --> the hikers need to close 12 miles of distance before they can meet each other

y = x + 1.2

t = 2 hours

The general rate equation is D = RT. Thus, you can get the distance travelled by each hiker if you multiply their rates by the time it takes them to meet.

x * t + y * t = d

x * t + (x + 1.2) * t = d

2x + 2(x + 1.2) = 12 --> Substitute your variables

2x + 2x + 2.4 = 12 --> Expand

4x + 2.4 = 12

4x = 9.6

x = 2.4 --> Simplify and solve

Thus, we get that the rate of the first hiker is 1.2 mph. Plugging that back into our expression for the second hiker, we get

y = x + 1.2 = 2.4 + 1.2 = 3.6

The second hiker is traveling at a rate of 3.6 mph.

To get the difference of the rates,

Difference = y - x = 3.6 - 2.4 = 1.2 mph

The difference between the hikers' rates is 1.2 mph.

Alternatively, if you were looking for the difference between their rates, you didn't need to solve for x and y at all. Using the previous setup,

x = rate of the first hiker

y = x + 1.2

Difference = y - x = (x + 1.2) - x = 1.2 mph