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.
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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