SOLUTION: using the pythagorean theorem formula two trains leave the same city at the same time. one heads dues west and one due noth one train travels 5 miles per hour faster than the o

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Question 418478: using the pythagorean theorem formula
two trains leave the same city at the same time. one heads dues west and one due noth one train travels 5 miles per hour faster than the other. After 2 hours they are 50 miles apart. Find the speed of each train.
so far i have (2r)^2+ (2r+10)^2=50^2
Answer by dnanos(83) About Me  (Show Source):
You can put this solution on YOUR website!
Let x the one speed and x+5 the speed of the other train...
Multiply each speed with the time (2 hours)related to it to obtain the miles they have done.
Then we use the Pythagorean theorem.
%282%28x%2B5%29%29%5E2%2B%282x%29%5E2=50%5E2
4%28x%5E2%2B10x%2B25%29%2B4x%5E2=50%5E2
4x%5E2%2B40x%2B100%2B4x%5E2=2500
8x%5E2%2B40x%2B100-2500=0
8x%5E2%2B40x-2400=0
divide by 8
x%5E2%2B5x-300=0
Use the formula x=%28-b%2B-sqrt%28b%5E2-4ac%29%2F2a%29 for a=1,b=5,c=-300
to obtain
x=%28-5%2Bsqrt%285%5E2%2B4%2A1%2A300%29%2F2%29 OR x=%28-5-sqrt%285%5E2%2B4%2A1%2A300%29%2F2%29
We get
x=%28-5%2B35%29%2F2
omit the negative solution as non geometrical
x=30/2
x=15 is the first speed.
and 15+5=20 the other.