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Question 1125946: The average speed of a plane is eight times as great as the average speed of a train.
the plane 8 3/4 hours less than the train to travel 1050 km find the average speed of the train
Found 4 solutions by Theo, greenestamps, josgarithmetic, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the average speed of a plane is 8 times the average speed of a train.
let the average speed of the train be equal to R.
the average speed of the plane is therefore 8 * R.
the plane take 8 and 3/4 hours less than the train to travel 1050 kilometers.
let the time the train takes be equal to T.
then the time the plane takes is equal to T - 8.75
find the average speed of the train.
equation to use is rate * time = distance.
for the train, the equation becomes R * T = 1050
for the plane, the equation becomes 8 * R * (T - 8.75) = 1050
these are two equations that need to be solved simultaneously.
we'll use substitution.
solve for T in the first equation to get T = 1050 / R.
replace T in second equation with 1050 / R to get:
8 * R * (T - 8.75) = 1050 becomes 8 * R * (1050 / R - 8.75) = 1050.
simplify to get 8 * R * 1050 / R - 8 * R * 8.75 = 1050.
multiply both sides of this equation by R to get:
8 * R * 1050 - 8 * R * 8.75 * R = 1050 * R
combine like terms to get:
8400 * R - 70 * R^2 = 1050 * R
add 70 * R^2 to both sides of the equation and subtract 8400 * R from both sides of the equation to get:
0 = 1050 * R - 8400 * R + 70 * R^2.
combine like terms and reorder the terms in descending order of degree and flip sides to get:
70 * R^2 - 7350 * R = 0
factor to get:
70 * R * (R - 105) = 0
divide both sides of the equation by 70 to get:
R * (R - 105) = 0
solve for R to get R = 0 or R = 105.
R is obviously not 0, so R needs to be 105 kilometers per hour or not at all.
when R = 105 kilometers per hour, the equation for the train becomes 105 * T = 1050.
solve for T to get T = 10.
when R = 105 kilometers per hour, 8 * R equals 840 kilometers per hour.
the equation for the plane becomes 840 * (T - 8.75) = 1050.
since T is equal to 10, this equation becomes 840 * (10 - 8.75) = 1050.
simplify to get 840 * 1.25 = 1050 which becomes 1050 = 1050.
this confirms the solution of R = 105 and T = 10 is correct.
the problems asks for the average speed of the train.
the solution is the average speed of the train is 105 kilometers per hour.
Answer by greenestamps(13198)  (Show Source):
Answer by josgarithmetic(39615)  (Show Source):
Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website! The average speed of a plane is eight times as great as the average speed of a train.
the plane 8 3/4 hours less than the train to travel 1050 km find the average speed of the train
This problem is definitely not as long, confusing, and complex as one person who responded makes it out to be
With the speed of the train being S, we get the speed of the plane as 8S
We then get the following TIME equation: 
Solve this for S, the speed of the train and you should get: 
That's ALL!! You don't have to make a MOUNTAIN out of a MOLEHILL to get the answer!
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