# MATH Algebra

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The speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 250 miles. Find the speed of each train.
What is the speed of passenger train? ____mph
What is the speed of freight train? _______ Mph

10) A long distance trucker travels 88 miles in one direction during a snowstorm. The return trip in rainy weather was accomplished at double the speed and took 2 hours less time. Find the speed going
The speed going was ____ mph.

• MATH Algebra -

P = speed of passenger train.
F = speed of freight train.
================
P+6 = F
distance = rate x time or rearrange to
time = d/r
For P train time = 280/P
For F frain time = 250/F
The times are equal so
280/P = 250/F but you know P = F + 6 so substitute F + 6 for P to obtain
280/(F+6) = 250/F
solve for F.

• MATH Algebra -

Speed forward direction = F
Speed return trip = R
====================
R = 2F
The time it takes for forward is
t = d/r = 88/F
The time for return is
t = d/r = 88/R or 88/2F
IF the times were equal (they aren't) then
88/F = 88/2F BUT it takes the return trip 2 hours less; therefore, we must add 2 hours to the return trip to make the times equal.
88/F = (88/2F) + 2
solve for F, the speed in the forward direction.

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