Question 1027306
rate * time = distance.


when r = rate and t = time and d = distance, this formula becomes:


r * t = d


when r = 10 miles per hour, the formula becomes:


10 * t = d


when r = 30 miles per hour and t is 2 less, the formula becomes:


30 * (t-2) = d


you have 2 equations that need to be solved simultaneously.


those equations are:


10 * t = d
30 * (t-2) = d


subtract the second formula from the first formula and you get:


10 * t - 30 * (t-2) = 0


simplify to get:


10 * t - 30 * t + 60 = 0


combine like terms to get:


-20 * t + 60 = 0


add 20 * t to both sides of the equation and you get:


60 = 20 * t


solve for t to get:


t = 3 hours.


t-2 = 1 hour.


when she bikes at 10 miles per hour, it takes her 3 hours.


r * t = d


10 * 3 = 30 miles.


when she drives at 30 miles per hour, it takes her 1 hour.


30 * 1 = 30 miles.


it's the same distance of 30 miles as it should be.


the solution is that she travels 30 miles to town.