SOLUTION: A train travels 80 mi in the same time that a light plane can travel 280 mi. If the speed of the plane is 100 mi/h faster than that of the train, find each of the rates.

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Question 964174: A train travels 80 mi in the same time that a light plane can travel 280 mi. If the speed of the plane is 100 mi/h faster than that of the train, find each of the rates.
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
______________rate_________time__________distance
train__________r____________t____________U
plane_________r+k___________t____________V

UNKNOWNS: r, t
KNOWNS: k=100,U=80,V=280

system%28rt=U%2C%28r%2Bk%29t=V%29

t=U%2Fr
-
rt%2Bkt=V
r%28U%2Fr%29%2Bk%28U%2Fr%29=V
U%2BkU%2Fr=V
kU%2Fr=V-U
1%2Fr=%28V-U%29%2F%28kU%29
Their reciprocals are then also equal:
highlight%28highlight%28r=%28kU%29%2F%28V-U%29%29%29