Question #a8a49

1 Answer
Apr 13, 2017

Answer:

I normally use a "strange" approach in this cases...anyway I got 1 hour and 45 minutes.

Explanation:

Let us call the quantity of water in the pool #x# and the rates (in liter per hour) of the two pumps #r_1# and #r_2# so we get:
#r_1*6=x#
#r_2*10=x#
meaning that the rate times the time will give us the amount of water pumped out.
Let us use the two pumps together; we get:
#(r_1+r_2)t=x#
where #t# will be the requred time.
From the two previos equations we get:
#r_1=x/6#
#r_2=x/10#
that substituted into: #(r_1+r_2)t=x# gives us:
#(x/6+x/10)t=x#
#x(1/6+1/10)t=x#
or:
#(1/6+1/10)t=1#
#t=3.75# hours corresponding to 1 hour and 45 minutes.