Question 1139969
r * t = d
r = rate
t = time
d = distance


when d = 240 km, then r * t = d becomes r * t = 240


r is in km per hour.
t is in hours.


when she increases the speed by 10 km/hr, she can save a total of 20 minutes.


20 minutes / 60 = 1/3 of an hour.


r * t = 240 becomes (r + 10) * (t - 1/3) = 240 when she increase her speed by 10 kmph and reduces the time it takes by 1/3 of an hour.


you have 2 equations that need to be solved simultaneously.


they are:


r * t = 240
(r + 10) * (t - 1/3) = 240


simplify the second equation and leave the first equation as is to get:


r * t = 240
r * t - r/3 + 10 * t - 10/3 = 240


in the second equation, replace r * t with 240 to get:


240 - r/3 + 10 * t - 10/3 = 240


subtract 240 from both sides of this equation to get:


-r/3 + 10 * t - 10/3 = 0


multiply both sides of this equation by 3 to get:


-r + 30 * t - 10 = 0


solve for r from the first equation to get r = 240 / t


replace r with 240/t in the equation of -r + 30 * t - 10 = 0 to get:


-240 / t + 30 * t - 10 = 0


multipky both sides of this equation by t to get:


-240 + 30 * t^2 - 10 * t = 0


divide both sides of this equation by 10 to get:


-24 + 3 * t^2 - t = 0


arrange the terms in descending order of degree to get:


3 * t^2 - t - 24 = 0


factor this quadratic equation to get:


(3t + 8) * (t - 3) = 0


solve for t to get:


t = -8/3 or t = 3


t can't be negative, so t = 3 looks like your solution.


when t = 3, r * t = 240 gets you r = 80


r * t = 240 becomes 3 * 80 = 240 which becomes 240 = 240, confirming the selection of r = 80 and t = 3 is correct.


(r + 10) * (t - 1/3) = 240 becomes (80 + 10) * (3 - 1/3) = 240 which becomes 90 * 8/3 = 240 which becomes 240 = 240, confirming the selection of r = 80 and t = 3 is correct again.


your solution is that her original speed was 80 km per hour.