SOLUTION: A dog is walking along a train track on e day, and traceled along that track onto a train bridge. When the dog was 1/4 of the way across the bridge, he heard a train whistle from a

Question 297107: A dog is walking along a train track on e day, and traceled along that track onto a train bridge. When the dog was 1/4 of the way across the bridge, he heard a train whistle from an oncoming train that was coming in the same direction the dog had already come. The dog bounded away form the train, and made it to the end of the bridge at exactly the same time as the train. What the dog didn't know, but what was also true, was that the dog could have bounded toward th train and made it to the "start" of the bridge at exactly the same time as the traing. The train was traceling at a speed of 30 mph. How fast was the dog traveling?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the dog's speed running
Let = the time for the train to just reach the bridge
Let = the length of the bridge in miles
-------------------------
In words:
(dog's speed) x (time for train to reach bridge + time for train to cross bridge) = (3/4)x(the length of the bridge)
As an equation:
(1)
---------------------------
In words:
(dog's speed) x (time for train to reach bridge) = (1/4)*(length of bridge)
As an equation:
(2)
---------------------------
In words:
(train's speed plus dog's speed) x (time for train to reach bridge) = (distance train travels to reach bridge plus distance dog runs)
As an equation:
(3)
----------------------------
This is 3 equations and 3 unknowns, so it's solvable
(1)
(1)
(1)
and
(2)
and
(3)
(3)
(3)
I can substitute (2) in (1)
(1)
(1)
(1)
(1)
The dog was running 15 mi/hr
check answer:
(2)
(2)
(2)
Substitute in (3)
(3)
(3)
(3)
OK

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