SOLUTION: The difference in the average speed of two trains is 16 miles per hour. The slower train takes 2 hours longer to travel 170 miles than the faster train takes to travel 150 mile

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Question 953335: The difference in the average speed of two trains is 16 miles per hour. The slower
train takes 2 hours longer to travel 170 miles than the faster train takes to travel
150 miles. Find the speed of the slower train
Answer by josgarithmetic(39800) About Me  (Show Source):
You can put this solution on YOUR website!
____________________speed__________time___________distance
SLOW________________r______________t+2____________170
FAST________________r+16___________t______________150

Implied variables;
RT=D uniform travel rates


Two equations in two unknown variables.

t=150%2F%28r%2B16%29
;
r%28%28150%2F%28r%2B16%29%29%2B2%29=170
150r%2F%28r%2B16%29%2B2r=170
150r%2B2r%28r%2B16%29=170%28r%2B16%29
150r%2B2r%5E2%2B32=170r%2B170%2A16
2r%5E2%2B32=20r%2B170%2A16
r%5E2%2B16=10r%2B170%2A8
r%5E2-10r%2B16-170%2A8=0
highlight_green%28r%5E2-10r-1344=0%29


PREPARE FOR GENERAL SOLUTION FOR QUADRATIC EQUATION
Discriminant: 100%2B4%2A1344=5476=%2874%29%5E2
;
r=%2810%2B-+74%29%2F2, obviously the PLUS form is needed.
r=%2810%2B74%29%2F2
highlight%28r=42%29