how do u use fractions to solve problems .?

Question

ahmed takes 2 h to mow his lawn. His brother, Sami takes 4 h. What fraction of the does each mow in 1h?

bob fill a water tank in 4min using a large hose. He takes 6 min using a smaller hose. How long will he take if he uses both hoses?

Bob can deliver 500 handbills in 2h. Althea can deliver the same # in 3 h. How long will they take to deliver 500 handbills if they work together?

Bob and milan are office cleaners. Bob earns 10$/h and takes 8 h to clean an office.
Milan earns $8/h and takes 10 h to clean it.
How long will it take bob and milan to clean the office together?
What is the cost of cleaning the office using only bob? only milan? bob and milan together?

Answer 1

1) ahmed in 1 hour = 1/2 of lawn Sami = 1/4 of lawn

2) in 1 min using both hoses the tank will be 1/4 + 1/6 full
or tank will be 5/12 full
so in 12/5 mins the tank will be full
Answer is 2.4 minutes

3) Answr is 1/(1/2+ 1/3) = 1.2 hours

4) Time = 1/(1/8 + 1/10) = 80/18 = 40/9 hours
Cost only bob = 80$
only Milan = 80$

both together = 18*40/9 = 80 $

Answer 2

1. 1/2 and 1/4

For the rest of these I use that the Time together or T divided by the time Alone or A of each person = one whole job done

It looks like this T/A + T/A = 1. Each fraction stands for each of the individual workers. If you had more workers you would add another T/A.

2. Let T = Time together
T/4 + T/6 =1
Multiply by 12
3T + 2T= 12
5T = 12
T = 2 and 2/5 min

2. T = Time together
Even though you have 500 handbills to deliver it is still one job to get done.
T/2 + T/3 = 1
Multiply by 6
3T +2T = 6
5T = 6
T = 6/5 or 1 and 1/5 hours

4) T is time together
T/8 + T/10 = 1
Multiply by 40
5T + 4T = 40
9T = 40
T = 40/9 or 4 and 4/9 hours

Cost: Bob alone is $10*8=$80
Milan = $8*10 = $80
Together
$10(40/9) +$8(40/9)=
400/9+320/9
720/9
$80

Answer 3

1. I don't quite understand this...

for the rest of the problems just use ratio and proportion or so called fractions as you said...

2.

given: 4 min and 6 min.

1/4 + 1/6 = 1/ x

x= 2.4 min

3.

given: 2h and 3 h

500/2 + 500/3 = 500/ x

x= 1.2 h

4.

given: bob - 10$/h in 8 h
milan - 8$/h in 10 h

how long together?

1/8 + 1/10 = 1/x

x= 4.44 h

cost only bob?
10 x 8 = $80

cost only milan?
8 x 10 = $ 80

cost bob and milan ?

(4.44 x 10) + (4.44 x 8) = $80

therefore its either you let bob and milan work together or bob only or milan only, you will pay the same cost for particular situation.

Answer 4

for the frst 1 i read i think u can use x
let the thing which is unknown b x and u will automaticaly get the answer.