If one-half of one interger is subtracted from three-fifths of the next consecutive intger, the diffrence is 3

Question

What are the two intergers?

Also-
A passenger train can travel 325 mi. in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25m/h faster then the speed of the freight train. find the speed of each.. Any conclusions.

Answer 1

The first question is really easy. Just transform your words into numbers.

(3/5)(x+1) - (1/2)x = 3. Solve for x. About ten people have already done this, so I'm sure you get it. Your two integers are obviously "X" and "X+1".

The second one is a bit more fun. I would use this equation, r = (d/t). Rate equals distance over time. The two trains have two rates. The time is the same, and the distances are different.

Time1 = 325/(r+25) That's the passenger train.

Time2 = 200/r That's the freight train.

Now, Time1 and Time2 are equal, so:

200/r = 325/(r+25) !!!!!!!!!!!!!!!!!!!!! WOW!

Now solve for r. Here's a little hint at solving this, just in case:

I often just flip the fractions when the variables are stuck on the bottom. It's allowed.

r/200 = (r+25)/325

r = 40mph r+25 = 65mph

The end.

Answer 2

(3/5)(n + 1) - (1/2)n = 3. Multiply both sides by 10 and get
6(n + 1) - 5n = 30; therefore (6-5)n + 6 = 30, or n = 24.
The integers are 24 and 25.
Proof - (3/5)25 - (1/2)24 = 15 - 12 = 3

speed * time = distance, so time = distance / speed .Let s be the speed of the freight train; then s + 25 is the speed of the passenger train, and
325 / (s+25) = 200 / s; thus 325 s = 200(s + 25) = 200 s + 5000.
Then 125 s = 5000, or s = 40.
Conclusions:
The speed of the freight train is 40 mph.
The speed of the passenger train is 65 mph.
The time in question is 5 hours.
Proof - 325 miles / 65 mph = 5 hours,
and also 200 miles / 40mph = 5 hours.

Answer 3

Let the integers be x and (x+1)

3/5 (x+1) - x/2 = 3

This is the equation you need

Multilpy out

3x/5 + 3/5 -x/2 = 3

Multiply both sides by 10 to get rid of the denominators

6x + 6 - 5x = 30

collect numbers on one side and xs on the other

x = 24. So next integer is 25

Check

15 - 12 = 3.......It works! so it's probably right

The train Qu.

For every hour that they travel, the passenger train goes 25 miles further than the freight tfain.

The journeys of 200 m and 325 miles take 5 hours .....

325 - 200 = 5 times 25

the slow train goes 200 miles in 5 hrs,

so it travels at 200/5 mph

=40 mph

The passenger train goes at 65mph

Check that 5 times 65 = 325...

Conclusion....It is quicker to travel by fast trains. That is the only thing I can conclude and I'm looking at this question through the eyes of a teacher. The bit about the conclusion is a very strange question.

You might like to ask your teacher why it was asked?

Answer 4

1. Call the first integer x
3/5*(x+1) - 1/2*x = 3
0.1x + 0.6 = 3
0.1x = 2.4
x = 24
Integers: 24, 25

2. Let speed of passenger train = a and speed of freight train be b
We know that distance/speed = time, so 325/a = 200/b (equation 1)
In addition, a - b = 25
This implies a = b + 25 (equation 2)
Substitute equation 2 into equation 1:
325/(b+25) = 200/b
Cross-multiply: 200b + 5000 = 325b
125b = 5000
b = 40 mi/h
a = 40+25=65 mi/h
Moreover, time taken = 325/65 = 5 h

Conclusions: Speed of passenger train = 65 mi/h; speed of freight train = 40 mi/h; time taken for vehicles to cover the distances, namely 325 mi for passenger train and 200 mi for freight train, is 5 hours.

Answer 5

rosie has the equation for the first problem and the equation for the second problem is 2x + 25 = 525

let the speed of the freight train = x
let the speed of the passenger train = x + 25

x + x = 2x and 325 + 200 = 525 or the total distance traveled by both trains

Isolate the variable and solve for x add 25 to get the speed of the passenger train.

Answer 6

edit: nevermind my answer was wrong