I am horrible with word problems. Can anyone help me with these too please show work so I can understand it.

Question

1. If 1/2 of one integer is subtacted from 3/5 of the next consecutive integer and the difference is 3. What are the two integers?

2. A passenger train can travel 325 mi. in the same time a frieght train takes to travel 200 mi. If the passenger train is 25 mi./h faster than the speed of the frieght train, find the speed of each.

3. Ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days what was the driving time each day?

Answer 1

let the consecutive integers be x and x+1 resply
3/5(x+1)-1/2x=3
3/5x-1/2x=15/5-3/5
6/10x-5/10x=12/5
x=10(12/5)=24
check
1/2 of 24=12
3/5(25)=15 and 15-12=3

2.
let the speeds of the passenger train and the
freight train be x+25 and x mph resply
325/(x+25)=200/x
cross multiplying
325x=200x+5000
125x=5000
x=40
speed of the passenger train is 60 mph and that
of the freifght train is 40 mph

3.let the time of journey on
the 1st and 2nd day be x+2 and x hrs resply
360/(x+2)=270/x
cross multiplying
360x=270x+540
90x=540
x=6
the driving times were 8 hrs and 6 hrs

Answer 2

1.) 1/2 of one integer (x) is subtracted from 3/5 of the next consecutive integer (x+1) and the difference is 3.
So, write the formula as:
3/5 (x+1) - 1/2 x = 3

Multiply out the parenthesis:
3/5 x + 3/5 - 1/2 x = 3

Add -3/5 to both sides:
3/5 x - 1/2 x = 2 + 2/5

Combine:
6/10 x - 5/10 x = 2 + 2/5
1/10x = 12/5

Multiply both sides by 10:
x = 120/5 = 24

Check:
3/5 * 25 - 1/2 * 24= 3
15 - 12 = 3 (correct!)

2.) A passenger train can travel 325 mi. in the same time a frieght train takes to travel 200 mi. If the passenger train is 25 mi./h faster than the speed of the frieght train, find the speed of each.

Velocity = distance/time
v(passenger train) = 325/x
v(freight train) = 200/x
v(passenger train) = v(freight train) + 25

Substitute the velocities:
325/x = 200/x + 25

Multiply both sides by x:
325 = 200 + 25x

Subtract 200 from both sides:
125 = 25x

Divide 25 from both sides:
x = 5 hours

Speed:
v(passenger train) = 325/x = 65 mph
v(freight train) = 200/x = 40 mph

3.) Ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days what was the driving time each day?

Write down what you know:
Velocity = distance over time
v(day one) = v(day two)
t(day one) = t(day two) + 2 (the 2 hours longer part)
d(day one) = 360 mi
d(day two) = 270 mi
d(1)/t(1) = d(2)/t(2)

Substitute:
360 mi / t(1) = 270 mi / t(2)

Substitute what you know about t(2):
360 mi / (t(2)+2) = 270 mi / t(2)

Flip the fractions:
(t(2)+2)/360 = t(2) /270

Multiply both sides by 1080 (common denominator)
(t(2)+2)/360 * 1080 = t(2) /270 * 1080
3* (t(2)+2) = 4* t(2)

Multiply out parenthesis:
3t(2) + 6 = 4t(2)

Subtract 3t(2) from both sides:
6 hours = t(2)
t(1) = t(2) + 2 = 8 hours

Check:
v = d/t
360 / 8 = 270 / 6
45 = 45 (correct!)

Answer 3

step by step ....
1 .... 3/5(n+1) - 1/2 (n) = 3 ( *10) = 6(n+1) - 5n = 30
6n + 6 - 5n = 30 n + 6 = 30 n = 24

2. (f+25)t = 325
f * t = 200 so f = 200 / t .... (200 / t + 25)t = 325
200 + 25t = 325 25t = 125 t = 5

3. (t+2)* mph = 360
t * mph = 270 (t mph + 2mph) - (t mph) = 90
2 mph = 90 mph = 45



proof : 1) 3/5 (25) - 1/2 (24) = 3 15 - 12 = 3

2) 325 / 5 = 65 200 / 5 = 40 65 - 40 = 25

3) 360 / 45 = 8 270 / 45 = 6 8 - 6 = 2

Answer 4

I think I've got #3.

Total miles on day 1 - total hours on day 2
=360-270
=90

Therefore it took her 2 hours to drive 90 miles.

So she was travelling at 45 miles per hour.

So on the first day she travelled 360 miles at 45 miles per hour
=360 miles/x hours = 45 miles/1hour

Cross multiply.

360 = 45X
X = 8 hours.

On the first day she travelled for 8 hours.

On the second day she travelled 6 hours because on the first day she travelled 2 hours longer.

Answer 5

answer to #1 is 4 & 20
work u have to find a multiple of 5. ( 20).now take 3/5 away from 20. u get 5

now u find a multiple of 2.(4) and take 1/2 away. u get 2

now 2-5 is? 3!!!!

now #2. i think something is missing from this snetence

#3. something is also incomlpete. u have to kno how many mile per hour. but it doen't say

sorry i could only do 1

Answer 6

Trying to get us smart people to do your homework i see.