Alan​ Ben, are 14.8 miles apart and walking towards each other. They meet in 4hours. Find the rate of each hiker if Ben walks 0.9 mph faster than Alan.

Question

I don't know how to do it. can u help please. and it needs 2 answers

Answer 1

Hi Taghrid, this is a D(istance) = R(ate) * T(ime) problem. We know the distance traveled is 14.8 miles. We also know the time they walk is 4 hours. Last we know that Ben walks .9 mph faster than Alan.

 

We can set up an equation based on D = R * T.

 

Let x be the rate for Alan, then x + .9 is the rate for Ben.

 

The distance Alan covers in 4 hours is: 4x.

 

The distance Ben covers in 4 hours is: 4 * (x + .9)

 

The total distance traveled by both is 14.8 miles.

 

The equation:

 

4x + 4 * (x + .9) = 14.8

 

4x + 4x + 3.6 = 14.8

 

Combine terms and subtract 3.6 from both sides:

 

8x = 11.2

 

Divide both sides by 8:

 

x = 1.4

 

Alan's rate of travel is 1.4 mph. 

 

Ben's rate of travel is 1.4 + .9, or 2.3 mph.

 

Check:

 

4 * 1.4 + 4 * (1.4 + .9) = 14.8

 

5.6 + 9.2 = 14.8

 

14.8 = 14.8

 

Values check.

 

Questions?