Find the rate of each

Question

Two? hikers, Alan and? Ben, are 18 miles apart and walking towards each other. They meet in 5 hours. Find the rate of each hiker if Ben walks 0.6 mph faster than Alan.

Answer 1

If Alan walks A miles, then Ben walks 18-A miles

Let r = Alans rate, .. Ben's rate is A+.6

 

From the distance formula d=rt we have two equations

 

1)  A = 5r                 Alan's distance = 5 hrs(rate)

2) 18-A = 5(r+.6)     Ben's distance = 5 hrs(r+.6)

 

 Substitute 5r in place of A in equation 2

 

18-5r = 5r + 3     subtract 5r from both sides

-10r +18 = 3       subtract 18 from both sides

-10r = -15           divide both sides by -10

r = 1.5 mph

 

Alan walks at 1.5 mph

Ben walks at r+.6 = 2.1 mph