WORD PROBLEMS..Help.....?

Question

Work Problems
1. 2 buses left a gasoline station at the same time and traveled in opposite directions with 1 bus traveling at 80kph and the other as 108kph.After how many hours will the 2 buses be 329 kilometers apart?
2. Raymond can load the truck in 40 minutes.If his son Alvin helps him,t takes them 15 minutes.How long will it take Alvin to finish alone?
3. 2 trains leave the same trminal at the same time and travel in opposite directions,with the 1st train traveling at a speed of 20km per hour faster than the other.After 5 hours,they are 700km apart.Find the speed each...
****Please give the Checking and the Solution

Answer 1

1. Let the time it takes them to travel 329km apart be t hrs.
Bus 1 distance traveled =80t
Bus 2 distance travel led =108t

329=80t +108t
329=188t
t = 1.75hrs

Raymond can load the truck in 40 minutes. This is a rate problem. Synonymous with a distance time speed question.
Load truck is Synonymous with distance
Let Raymonds rate of loading be R
Let Alvins rate of loading be A
For Raymond: Load truck/R = 40 ==> Load truck = 40R... (1)
For Raymond and Alvin: Load truck/(R + A) = 15
Load truck = 15(R + A)............ (2)
Equating 1 and 2 we have: 15(R + A) = 40R
15A = 40R - 15R = 25R ==> A = 25R/15 = 5R/3
For Alvin working alone it will take him:
Load truck/(5R/3) mins. = 3/5(Load truck/R).... (3)
From eq 1 above Load truck/R = 40mins ...substitutingin eq 3
For Alvin working alone it will take him:
3/5(40 mins) = 24 mins.

3) Let the speed of the second train be x km/hr.
The speed of the first train is (x + 20)km/hr
After 5hrs of travel time the total distance they both travelled is equal to 700 km. Therefore: 5x + 5(x + 20) = 700
10x + 100 = 700
x = (700 - 100)/10 = 60 km/hr.
For the first train it's speed is 60 + 20 = 80 km/hr.
The second train's speed is 60 km/hr.

Answer 2

1. Buses:
x = travel hours

80x + 108x = 329
188x = 329
x = 7/4 or 1 3/4

Answer: 1 3/4 hours or 1 hour, 45 minutes

Proof:
7/4 hr (80 kph + 108 kph) = 329 km
7/4 hr * 188 kph = 329 km
329 km = 329 km

2. Raymond and Alvin:
Let x = speed of Alvin in trucks per hour

Speed of Alvin:
1/4(3/2 + x) = 1
3/2 + x = 4
x = 8/2 - 3/2
x = 5/2 or 2 1/2

Time Alvin can finish alone:
= 1/(5/2)
= 2/5

Answer: Alvin can finish load a truck in 2/5 hr or 24 minutes.

Proof:
1/(3/2 + 5/2) = 1/4
1/4 = 1/4

3. The trains:
x = speed of one train, x + 20 = speed of the other train

Speed of one train:
5(x + x + 20) = 700
2x + 20 = 140
x + 10 = 70
x = 60

Speed of the other:
= 60 + 20
= 80

Answer: speed of one is 60; the other has 80

Proof:
5 hr (60 kph + 80 kph) = 700 km
5 hr * 140 kph = 700 km
700 km = 700 km

Answer 3

1. The buses separate at a rate of 188 kph. So to be 329 km apart, they must travel 329/188 hours.
2. These are "rate" problems, where you multiply capacity per time times time. Raymond has a load rate of 1 truck/40 minutes. Let Alvin's load rate be X. Then 1 truck/40 * 15 + X * 15 =
1 truck or 15/40+15X = 1 and x= 1truck/24 minutes.
3. This is alot like the first problem. They are separating at a rate of 2X+20 kph. With the given info: 5 hr *(2X+20) = 700.

Answer 4

OK

80t + 108t = 329
188t = 329
t = 1.75 hours

1 hour and 45 minutes.

Let's check
80 (1.75hours) + 108(1.75hours) = 329 k?
140k + 189k = 329k?
329k = 329k YES!!
=============
Both together load the truck in 15 minutes
Raymond himself loads the truck in 40 minutes

Together, they could load 2(15) + 2/3(15) trucks in the time it take Raymond to do 1.

So that must mean his son, in that 40 minutes, would be able to load 1 2/3 of a truck.

40 = 1 2/3x
24 =x

So Alvin can load one truck in 24 minutes by himself.

=========================

(s + s +20 )5 = 700
(2s + 20)5 =700
10s + 100 = 700
10s = 600
s = 60

So the slow train is traveling 60kph and the faster train is traveling 80kph.

Check
5(60) + 5(80) = 700?
300 + 400 = 700?
700 = 700 YES!

Hope that helps.

Answer 5

1. 329/(80 + 108) hurs = 329/188 hours = 1 hr 45 mts

2. 40x/(40 + x) = 15 => 25x = 600 => x = 24
alone Alvin in 24 mts.

3. 700/(2x + 20) = 5 => 10x = 600 => x = 60
slower one @ 60 km per hour
other one @ (60 + 20) kmh = 80 km per hour

Answer 6

1)D=329kmph.
S=108+80=188
T=D/S=329/188=1hr 45 min.
checking:-(188*105)/60=329

2)raymond's 1min work=1/40
let alvin's imin work=1/x
1/40+1/x=1/15
solving,i got x=24
so time taken =24min
check:-1/40+1/24=1/15

3.)D=700km
T=5h
let s=x and x+20
total S=x+x+20=2x+20
S=D/T=700/5=140
2x+20=140
2x=140-20=120
x=120/2=60
so,speed of first train=x+20=60+20=80kmph
speed of second train=x=60kmph
checking:-2*60+20=120+20=140

Answer 7

1.Bus 1=80x
Bus 2=108x

329=80x+108x
329=188x
1.75hrs

3. Train 2 speed = x
Train 1 speed = x+20

700=5(x+x+20)
700=10x+100
600=10x
60kph = train 2
80kph = train 1

Answer 8

1) 80t+108t=329
t=1.75 h.

2) 40-15 = 25 minutes .

3) Speed of train A = x
Speed of train B= X+5
Time = 5
X(t)+(x+25)(t)=700
5x+5x+125=700
x=57.5 Km/h
A=57.5 Km/h
B=82.5 Km/h

Answer 9

1. 1 hour 45 minutes
2. 24 minutes
3. 60kph and 80kph