SOLUTION: Karen went on a 48 mile trip to a soccer game. On the way back, due to road construction she had to drive 24 miles per hour slower. This made the trip take 1 hour longer. How fast

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Question 1150419: Karen went on a 48 mile trip to a soccer game. On the way back, due to road construction she had to drive 24 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Karen went on a 48 mile trip to a soccer game. On the way back, due to road construction she had to drive 24 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
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Similar problem:
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Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride?
1 solutions
Answer 771800 by Alan3354(65463) About Me on 2019-12-13 17:53:17 (Show Source):
You can put this solution on YOUR website!
Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride?
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r = his speed, t = the time he rode
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24/r = t
24/(r+6) = t-9
Solve for r

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let v be the rate to travel to the game, in miles per hour.

Then the rate returning back is (v-24) miles per hour.


Use a "time" equation


    48%2F%28v-24%29 - 48%2Fv = 1   hour.


From this equation, the solution is seen just even unarmed eye: v= 48 miles per hour.



CHECK.  48%2F48 = 1 hour is the time to go to the game, and

        48%2F%2848-24%29 = 2 hours is the time to go back.   2 hours - 1 hour = 1 hours.  ! Precisely correct !



But if you want to solve the equation (1) algebraically, you can do it.


Multiply both sides by v*(v-24);  get a quadratic equation; reduce it to its standard form

and then solve by any method you want / (you know).