Simple division word problems (Algebra)! Urgent!?

Question

So I need help with 5 division word problems, it'd pretty simple division but I lack at these kind of problems and I need some guidance. If someone can explain how to do these 5 problems and show the work, that would be amazing! Thanks to anyone who can help.

1. Two times the reciprocal of a number equals 28 times the reciprocal of 35. Find the number.

2. Sandra scored 72 points in 11 games of the basketball season. Find her average points per game. (Round to the nearest whole number if necessary)

3. A painter can finish painting a house in 3 hours. Her assistant takes 5 hours to finish the same job. How long would it take for both of them to complete the job if they were working together?

4. One pump can drain a pool in 7 minutes. When a second pump is also in use, the pool only takes 5 minutes to drain. How long would it take the second pump to drain the pool if it was the only pump in use?

5. Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 12 miles with the wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the wind?

Thanks again to whoever can help me further understand these problems.

MoKo · Accepted Answer

1)   2 * 1/x = 28 * 1/35

2/x = 28/35
2 = 28x / 35
70 = 28x
x= 70/28

2) 72 points / 11 games = 6.5 points/game = 7 points/game

3) 1 house/3 hours + 1 house/5 hours = 3 houses/15 hours + 5 houses/15 hours = 8 houses/15 hours = 0.533 houses/hour, take the reciprocal,therefore = 1.87 hours per house

4) say 7 gallons, pump 1 = 1 gallon per minute (gpm), therefore 7 minutes for 1 pump

7 gallons / (1 gpm + x ) = 5 min, therefore x = 2/5 gpm

7 gallons / 2/5gpm = 17.5 minutes

5)

y=time he ran
x= wind mph

y*5mph +y*x = 12 miles
y*5mph - y*x = 4 miles

two equations with two unknowns, solve for one then the other:

12/ (5+x) = y , plug this y into the second equation:

(60 -12x) / (5+x) = 4 miles
x= 40/16 mph
x= 2.5 mph

Tal · Answer

1. setting x=unknown #
you write the equation
2*(1/x)=28*(1/35)
2/x=28/35=4/5
then you cross multiply and get
4x=2*5=10
x=10/4=2.5

2. 72 points over 11 games
so the average is total points/total games=
72/11=
6 + 6/11=
about 7

3. the painter does 1/3 in an hour and the assistant does 1/5
setting one to completion and h=# hours you write
1=(1/3 + 1/5)h=(8/15)h
divide both sides by 8/15 and you get
h=1/(8/15)=15/8
15/8 hours

4. Setting x= # of min second pump takes alone
the second pump does 1/x per min
the pumps together do 1/5 per min
1/7 + 1/x=1/5
(7+x)/7x=1/5
5(7+x)=35+5x=7x
35=2x
x=17.5
It would take 17.5 minutes

5. saying Jim runs for h hours
and the wind blows him him x mph
h(5+x)=12
h(5-x)=4
3h(5-x)=12=h(5+x)
divide both sides by h to get
3(5-x)=5+x
15-3x=5+x
10=4x
2.5=x
the wind is blowing 2.5 mph

? · Answer

1) 2/x = 28/35 = 4/5
x = 5/2 = 2.5

2) 72/11 = 6.545
7 points

3) t/3+t/5 = 1
8t = 15
t = 15/8 hours = 1.875 hours

4) 5/7+5/t = 1
5t+35 = 7t
2t = 35
t = 17.5 minutes

5) 12/(5+w) = 4/(5-w)
60-12w = 20+4w
40 = 16w
w = 2.5 mph

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Simple division word problems (Algebra)! Urgent!?

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