Question

One pipe can fill a pond in 3 weeks, and second pipe can fill the pond in 5 weeks. However, evaporation and seepage can empty the pond in 10 weeks. If both pipes are used, how long
will it take to fill the pond?

I was hoping someone could help me also understand how to set up equations in this context also

Answer 1

these problems are almost like
rate * time = distance
in this case

rate * time = filled pond
where rate is measured in ponds per week
and time is measured in weeks

Answer 2

So I'm thinking 3t+5t = 1?

Answer 3

3t says: 3 times number of weeks

rates are fractions (or ratios)
example 10 miles per hour is 10 miles /1 hour

here you have filled ponds per week

Answer 4

in other words 3t does not make sense.

Answer 5

Oh woops, I tried the equation (1/3+1/5)t=1 and it felt sort of correct but I'm not totally sure

Answer 6

Or wait maybe (1/3+1/5)t-1/10=1

Answer 7

close, 1/10 is also a rate. you should multiply by it by t

Answer 8

notice if you fill a pond in 3 weeks, ⅓ ponds/week * 3 weeks = 1 pond
that makes sense.

Answer 9

Oh I see
(1/3+1/5-1/10)t=1