Question 1133497: A trip to Mount Pilatus ,in Lucerne,Switzerland involves riding an incline railroad up to the top of the mountain,spending time at the top,then coming down the opposite side of the mountain in an aerial tram.The distance traveled up to mountain is 7.5 kilometers and the distance traveled down the mountains is 8.7 kilometres.The speed coming down the mountain is 1.2 times the speed going up..If the Lieblich's stayed at the top of the mountain for 3 hours and the total time of their outing was 9 hours,find the speed of the inclined railroad.
Found 3 solutions by ikleyn, Theo, MathTherapy:
Answer by ikleyn(52803)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! let D equal the speed going up the inclined railroad.
let E equal the speed cocming down on the tram.
let I equal the time it takes to go up the railroad.
let J equal the time it takes to come down onm the tram.
the distance going up the railroad is 7.5 kilometers.
the distance coming down on the tram is 8.7 kilometers.
rate * time = distance.
going up, the formula becomes D * I = 7.5
coming down, the formula becomes E * J = 8.7
your two formulas that have to be solved simultaneously are:
D * I = 7.5
E * J = 8.7
the speed coming down on the tram is 1.2 * the speed going up on the train.
therefore E = 1.2 * D.
the two formulas become:
D * I = 7.5
1.2 * D * J = 8.7
the total time of their outing is 9 hours.
they stayed on top of the mountain for 3 hours.
therefore the total traveling time was 6 hours.
that makes I + J = 6
solve for I to get I = 6 - J
the two formulas now becomes:
D * (6 - J) = 7.5
1.2 * D * J = 8.7
simplify the equations to get:
6 * D - D * J = 7.5
1.2 * D * J = 8.7
multiply both sides of the first equation by 1.2 to get:
7.2 * D - 1.2 * D * J = 7.5
1.2 * D * J = 8.7
add the two equations together to get:
the + 1.2 * D and the - 1.2 * D canceled out, leaving 7.2 * D = 17.7
divide both sides of this equation bhy 7.2 to get:
D = 17.7 / 7.2 = 2.4583333333...
E is equal to 1.2 times that, so E = 2.95
your two original formulas are:
D * I = 7.5
E * J = 8.7
when D = 2.4583333333....k, solve for I to get I = 7.5 / 2.458333333..... = 3.050847458 hours.
when E = 2.95, solve for J to get J = 8.7 / 2.95 = 2.949152543 hours.
add up I and J to get 6, which is the total traveling time.
the speed of the trian is D which is equal to 2.4583333333..... kilometers per hour.
that's your solution.
why did i pick those letters?
my calculator stores values in lettered storage.
i picked those letters because those are the letters where i stored the intermediate results.
it makes doing the calculations a lot easier when you can store them rather than always writing them down each time.
the calculator i used is the TI-84 Plus.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! A trip to Mount Pilatus ,in Lucerne,Switzerland involves riding an incline
railroad up to the top of the mountain,spending time at the top,then coming down the opposite side of the mountain in an aerial tram.The distance traveled up to mountain is 7.5 kilometers and the distance traveled down the mountains is 8.7 kilometres.The speed coming down the mountain is 1.2 times the speed going up..If the Lieblich's stayed at the top of the mountain for 3 hours and the total time of their outing was 9 hours,find the speed of the inclined railroad.
Let speed going up the mountain be S
Then speed downward = 1.2S
Travel time: 9 - 3 = 6 hours
We then get the following TIME equation: 
7.5(6) + 8.7(5) = 6(6S) ------ Multiplying by LCD, 6S
45 + 43.5 = 36S
88.5 = 36S
S, or speed going up the mountain = 
It's that SIMPLE, nothing COMPLEX!!
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