SOLUTION: Mary makes monthly visits to her parents in Malacca, a distance of 240 km from Singapore.She finds that if she increases the speed by 10 km/hr , she could save a total of 20 minute

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Question 1139969: Mary makes monthly visits to her parents in Malacca, a distance of 240 km from Singapore.She finds that if she increases the speed by 10 km/hr , she could save a total of 20 minutes.
Find the original speed.
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source):
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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.

Answer by ikleyn(52771)   (Show Source):
You can put this solution on YOUR website!
.

Let r be the original speed under the question. Then you have this "time" equation - = hours. <<<---=== Every fraction on the left side is the time to cover the distance . . . To solve it, multiply both sides by 3*r*(r+10). You will get 720*(r+10) - 720r = r*(r+10) 7200 = r^2 + 10r r^2 + 10r - 7200 (r-80)*(r+90) = 0 The two root of the equation are r = 80 and r = -90, but only positive r = 80 km/h makes sense. ANSWER. The original speed was 80 kilometers per hour. CHECK. = 3 hours; = hours = 2 hours and 40 minutes; the difference is 20 minutes. ! Correct !

Solved

Using "time" equation is the STANDARD way to solve such problems.

From this solution, learn on how to write, how to use and how to solve a "time" equation.

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Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website!

Mary makes monthly visits to her parents in Malacca, a distance of 240 km from Singapore.She finds that if she increases the speed by 10 km/hr , she could save a total of 20 minutes.
Find the original speed.

Actual time taken, with S being the speed:
Hypothetical time, with S + 10 being the hypothetical speed:
Equation you need: ------ Converting 20 minutes to an hour(s)
3(240)(S + 10) - 3(240S) = S(S + 10) ------- Multiplying by LCD, 3S(S + 10)

Factors of the above TRINOMIAL: + 90 and - 80
Original speed or OR S = - 90 km/h (ignore)