Question

Two joggers set out at the same time from their homes which are 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, what is the rate of each?

Answer 1

Let A and B be two joggers

Speed of A = x mph
Speed of B = x+6 mph (Because rate of one is 6 mph faster than other)
Time =1.5 hour (1 hour 30 minutes)
Total Distance =24 miles

Now:
Distance covered by A in 1.5 hour = (x) * 1.5        (Distance=Speed*Time)
Distance covered by B in 1.5 hour = (x+6) * 1.5

Thus
      Total Distance = Distance covered by A + Distance covered by B
=>  24 = {x * 1.5} + {(x+6) * 1.5}
=>  24 = [x + x + 6] 1.5
=>  24 = [2x+6]1.5
=>  24 = [x+3] 2*1.5
=>  8   = x+3
=>  x   = 5

Therefore
Speed of A = x = 5 mph
Speed of B = x+6 = 5+6=11 mph