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

Question 1150320: 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 jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

x = Karen's speed, in mph, going from her house to the soccer game
y = time it took, in hours, to go from Karen's house to the soccer game
d = 48 is the distance traveled in miles

When Karen goes from her house to the game, then we can set up this equation below:

Plug in d = 48, r = x, and t = y.

Divide both sides by x to isolate y.

We'll use this equation later

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When heading back home, she takes 1 hour longer. So instead of driving for y hours, she drives for (y+1) hours. This is because her speed drops from x mph to (x-24) mph. The distance d is still the same at 48 miles.

Plug in r = (x-24) and t = (y+1)

Next, plug in y = 48/x, which was that equation we found earlier. At this point, we need to solve for x. But first let's do a bit of algebra to simplify this equation.

Use the distributive property

Use the distributive property again

Multiply both sides by x so that you clear out the fraction.

Note how the fraction is eliminated after using the distributive property.

Subtract 48x from both sides

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In order to solve , we can use the quadratic formula.

Compare that equation to the general quadratic and we see that a = 1, b = -24, c = -1152.

Plug those a,b,c values into the quadratic formula below. Then simplify.

or

or

or

or

or

or

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A negative speed does not make sense, so we ignore x = -24.
The only practical solution is x = 48.

So she drives from her house to the soccer game at 48 mph.
If x = 48, then y = 48/x = 48/48 = 1. This means it takes her 1 hour to drive from her house to the soccer game.

Also, if x = 48, then x-24 = 48-24 = 24 is her speed coming back home. The time it takes to drive back home is t = d/r = 48/24 = 2 hours, which fits with the description that she took one hour longer (compared to her journey from her house to the soccer game).

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Answer: 48 miles per hour

Answer by MathTherapy(10557) (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?

EVERYTHING that the other person did is way too COMPLEX and WAY TOO time-consuming.
If I were you, I'd simply IGNORE it!
This is the correct way to do the problem:
Let the outgoing speed be S
Then the return speed = S - 24
The return trip took 1 hour longer, so we get the following TIME equation:
48(S - 24) = 48S - S(S - 24) ------ Multiplying by LCD, S(S - 24)

(S - 48)(S + 24) = 0
S, or OR S = - 24 (ignore)
That's IT!! No NOVEL has to be written on this!
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