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Solution 1
Let "r" be the Andy's rate, in kilometers per hour.
Then the Billy's rate was (r-5) km/h.
Abby covered the distance r*3 in three hours.
Billy covered the distance (r-5)*(3 + 1/3) (notice that 1/3 = 1/3 of an hour = 20 minutes).
The distance is the same, which gives you an equation
3r = (10/3)*(r-5).
Simplify and solve for r. First step is to multiply both sides by 3 and open parentheses:
9r = 10r - 50 ====> 50 = 10r - 9r ====> r = 50.
Thus Andy's rate was 50 km/h.
Hence, the distance between the towns was 3*50 = 150 km.
Solution 2
Let D be the distance between the towns.
Andy's rate was kilometers per hour.
Billy's rate was kilometers per hour. (Notice that = hours).
The difference of the rates was 5 km/h, according to the condition.
It gives you an equation
- = 5, or, which is the same
- = 5.
Multiply both sides by 30. You will get
10D - 9D = 5*30 ====> D = 150.
You got the same answer: The distance is 150 kilometers.
Solved.