In a certain number of hours a woman traveled 6 km. If she had traveled 3 km more per hour, it would have taken her 7 h less to make the journey. How many kilometers did she travel per hour? (Keep three significant digits.

We will define the following variables to solve the problem:
 s: normal speed
 t: normal time
 We write the following system of equations:
 6 = s * t
 6 = (s + 3) * (t-7)
 Rewriting the equation two we have:
 6 = s * t -7s + 3t -21
 Substituting:
 s = 6 / t
 6 = (6 / t) * t -7 (6 / t) + 3t -21
 Multiplying both sides by t:
 6t = 6t - 42 + 3t ^ 2 - 21t
 Rewriting:
 3t ^ 2 - 21t - 42 = 0
 We take the positive root:
 t = 7/2 + root (105) / 2
 t = 8.62 h
 We look for the value of the speed:
 s = 6 / t
 s = 6 / 8.62
 s = 0.696 km / h
 Answer:
 she did travel 0.696 kilometers per hour