SOLUTION: he speed of a freight train is 30 mph slower than the speed of a passenger train. The freight travels 140 mi in the same time that it takes the passenger train to travel 210 mi. Fi

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Question 1162390: he speed of a freight train is 30 mph slower than the speed of a passenger train. The freight travels 140 mi in the same time that it takes the passenger train to travel 210 mi. Find the speed of each train.
Found 4 solutions by josgarithmetic, greenestamps, MathTherapy, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
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Freighttrain
r-30, 140 miles, for some given time

Passengertrain
r, 210 miles, for the same given time

140%2F%28r-30%29=210%2Fr
.
.
.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is fine....

If you set up the problem a bit differently, it is easy to solve without formal algebra, using basic arithmetic.

The ratio of the speeds is x-30:x; the ratio of distances is 140:210.

%28x-30%29%2Fx+=+140%2F210

Simplify the fraction on the right:
%28x-30%29%2Fx+=+2%2F3

Now multiply numerator and denominator on the right by some number so that the difference between the numerator and denominator is 30 (as the expression on the left requires). Since the current difference between the numerator and denominator is 1, the number to multiply is 30:

%28x-30%29%2Fx+=+60%2F90

The speeds of the two trains are 60mph and 90mph.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
he speed of a freight train is 30 mph slower than the speed of a passenger train. The freight travels 140 mi in the same time that it takes the passenger train to travel 210 mi. Find the speed of each train.
Let speed of freight train be S

Then speed of passenger train = S + 30.

Freight and passenger trains' times: matrix%281%2C3%2C+140%2FS%2C+and%2C+210%2F%28S+%2B+30%29%29, respectively 

As their times are the same, we get the following DISTANCE equation: matrix%281%2C3%2C+140%2FS%2C+%22=%22%2C+210%2F%28S+%2B+30%29%29

matrix%281%2C3%2C+2%2FS%2C+%22=%22%2C+3%2F%28S+%2B+30%29%29 ------- Factoring out GCF, 70, in numerator

3S = 2(S + 30) ------ Cross-multiplying

3S = 2S + 60

3S - 2S = 60

Speed of freight train, or highlight_green%28matrix%281%2C4%2C+S%2C+%22=%22%2C+60%2C+mph%29%29

You should now be able to find the passenger train's speed.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
he speed of a freight train is 30 mph slower than the speed of a passenger train.
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Poorly worded.
The speed is not slower. The train is slower.
----
The speed ... is less ...
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I might be pedantic.