SOLUTION: Kristina went on a 260 mile trip to a soccer game. On the way back, due to road construction she had to drive 13 miles per hour slower. This made the trip take 1 hour longer. How f

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Question 1026592: Kristina went on a 260 mile trip to a soccer game. On the way back, due to road construction she had to drive 13 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
She drove how many mph on her way to the soccer game?
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Kristina went on a 260 mile trip to a soccer game. On the way back, due to road construction she had to drive 13 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?
She drove how many mph on her way to the soccer game?
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To the game DATA:
dist = 260 miles: rate = r mph ; time = 260/r hrs.
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From game DATA:
dist = 260: rate = r-13 mph ; time = 260/(r-13) hrs
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Equation:
from time - go time = 1 hr
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260/(r-13) - 260/r = 1 hr
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260r - 260r + 13*260 = r(r-13)
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r^2 - 13r - 13*260 = 0
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(r-65)(r+52) = 0
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Positive solution:: rate = 65 mph
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
see the attached worksheet and follow the steps (circled numbers).

step 1 gives you the original 2 equations.

the first equation is r * t = 260

the second equation is (r - 13) * (t + 1) = 260

the first equation is the speed going (r) times the time it takes (t) to reach a distance of 260 miles.

the second equation reduces the speed by 13 miles per hour and increases the time by 1 hour.

step 2 simplifies the second equation.

step 3 adds 13 to both sides of the equation.

step 4 replaces r * t with 260 that it got from the first equation.

step 5 takes the r * t = 260 equation and solves for r.

step 6 replaces r with 260 / t in the second equation.

step 7 multiplies both sides of the equation in step 6 by t.

step 8 subtracts 260t and 260 from both sides of the equation and adds 13t^2 to both sides of the equation.

step 9 combines like terms from the equation in step 8 and reorders the terms in descending order of degree.

step 10 takes out the greatest common factor of 13.

step 11 factors the equation in step 10.

step 12 solves for t to get t = 4 and t = -5.

t = -5 is no good because it's negative, so the solution is t = 4.

going to the soccer game, t = 4 and d = 260 so the equation of r * t = d becomes:

r * 4 = 260

divide both sides of this equation by 4 to get r = 65.

she was driving 65 miles per hour to get to the soccer game and it took her 4 hours.

4 * 65 = 260.

on the way back, she was driving 52 miles per hour and it took her 5 hours.

5 * 52 = 260.

solution looks good.

solution is that she drove 65 miles per hours to get to the soccer game.

worksheet is shown below.