SOLUTION: James travels 550km by car and returns the same distance by train. The car travels 25km/h faster than the train and takes 75 minutes less time. What is the speed of the car in the

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Question 873342: James travels 550km by car and returns the same distance by train. The car travels 25km/h faster than the train and takes 75 minutes less time. What is the speed of the car in the nearest km/h?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
_________________speed______________time__________distance
CAR______________r+25_______________t-1%261%2F4_______%28r%2B25%29%28t-1%261%2F4%29=550
TRAIN____________r__________________t_____________rt=550

Two equations occur based on knowing the one-way distance.

CAR equation: %28r%2B25%29%28t-5%2F4%29=550
rt%2B25t-5r%2F4-125%2F4=550
rt%2B25t-5r%2F4-125%2F4=rt, the substitution using the TRAIN equation.
25t-5r%2F4-125%2F4=0
100t-5r-125=0
4t-r-5=0
r=4t-5 allowing for substitution now into the TRAIN equation.
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rt=550
%284t-5%29t=550
4t%5E2-5t=550
highlight_green%284t%5E2-5t-550=0%29 ----You want to solve this for time t, and use it to find the speeds of the train and CAR.
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discrim, 25%5E2%2B4%2A4%2A550=9425
discrim, 9425=25%2A377=5%5E2%2A13%2A29
highlight%28t=%285%2B5sqrt%28377%29%29%2F8%29 HOURS
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r=550%2Ft
r=550%2F%28%285%2B5sqrt%28377%29%29%2F8%29
r=%28550%2A8%29%2F%285%2B5sqrt%28377%29%29
r=%28110%2F8%29%2F%281%2Bsqrt%28377%29%29
r=%2855%2F4%29%2F%281%2Bsqrt%2877%29%29
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TRAIN speed, not quite yet in proper simplified radical form,
r%2B25=25%2B%2855%2F4%29%2F%281%2Bsqrt%28377%29%29
highlight%28r%2B25=25%2B55%2F%284%281%2Bsqrt%28377%29%29%29%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
James travels 550km by car and returns the same distance by train. The car travels 25km/h faster than the train and takes 75 minutes less time. What is the speed of the car in the nearest km/h?


Quadratic equation: S%5E2+-+25S+-+11000+=+0

Speed of car:  118.1231509 ≈ highlight_green%28118%29 km/h

You can do the check!! 



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