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Algebra_4
Chapter 97
Problem 1
Select a different problem
Example:
In the morning the passenger train made the trip in 3 hours
In the afternoon the freight train made the same trip in 7 hours.
Find the velocity of each if the velocity of the freight train
was 40 miles per hour less than the velocity of the passenger train.
In shorthand form the problem can be written as follows:
Freight train time t
f = 3 hours. (1)
Passenger train time t
p = 7 hours
The difference in velocities v
p = v
f + 40 (2)
Since they traveled the same distance, v
ft
f = v
pt
p (3)
Substituting equation (2) into equation (3) gives
v
ft
f = (v
f +40)t
p
or v
f(t
f - t
p) = 40t
p
Thus, the velocity of the freight train v
f = 40t
p/(t
f - t
p)
So The velocity of the freight train v
f = 40(3)/(7 - 3) = 30 miles per hour
and the velocity of the passenger train v
p = 30 + 40 = 70 miles per hour
