SOLUTION: Solve. If one half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is three. What are the two integers? Solve. A passenger

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Solve. If one half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is three. What are the two integers? Solve. A passenger      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 116814: Solve.
If one half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is three. What are the two integers?

Solve.
A passenger train can travel 325 miles in the same time a freight train takes to travel 200 miles. If the speed of the passenger train is 25 miles per hour faster than the speed of the freight train, find the speed of each.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If one half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is three. What are the two integers?
:
x = one integer; (x+1) = next consecutive integer, change fractions to decimals
one-half =.5; and three/fifths = .6
:
Write an equation for what it says:
.6(x+1) - .5x = 3
.6x + .6 - .5x = 3
.6x - .5x = 3 - .6
.1x = 2.4
x = 2.4/.1
x = 24 is the 1st integer, 25 is the next integer
:
Check solution in the statement:
"one half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is three.
.6(25) - .5(24)
15 - 12 = 3
:
:
Solve.
A passenger train can travel 325 miles in the same time a freight train takes to travel 200 miles. If the speed of the passenger train is 25 miles per hour faster than the speed of the freight train, find the speed of each.
:
Let x = speed of the freight train
then
(x+25) = speed of the pass train
:
It says the times for the two is the same. Write a time equation:
Time = distance/speed
Pass time = Freight time
325%2F%28%28x%2B25%29%29 = 200%2Fx
;
Cross multiply and you have:
325x = 200(x+25)
325x = 200x + 5000
325x - 200x = 5000
125x = 5000
x = 5000%2F125
x = 40 mph is the freight
then
40 + 25 = 65 mph is the pass train
:
We can check solutions by confirming that the times are, indeed, equal:
325/65 = 5 hr
200/40 = 5 hrs also
:
Was I able to make this easy for you to understand? Any questions?