First of all, we have to observe that the expression makes sense only if
otherwise, you'd have zero denominators, which are not allowed. So, assuming , let's sum the two fractions at the left hand side:
Again, since we're assuming , we can multiply both sides by to get
This equation has solutions and , but we can only accept the first, since 1 is a forbidden value.
So, the only solutions to this equation is
Answer:
points
Step-by-step explanation:
The first pump empties half the pond in 3 hours, so in 1/6 that time (1/2 hour), it empties (1/6)·(1/2) = 1/12 of the pond.
The second pump empties the other 5/12 of the pond in that half hour, so has a pumping rate of (1/2 h)/(5/12 pond) = (6/5 h)/pond.
The second pump could do the entire job alone in 1 hour and 12 minutes.
Answer:
Phone 1 will allow Ellie to talk the longest
Step-by-step explanation:
Phone 1:
(0.10x) + 6 = y
(0.10x) + 6 - 6 = 22 - 6
0.10/0.10x = 16/0.10
x = <u>160</u> minutes
Phone 2:
(0.25x) + 5 = y
(0.25x) + 5 - 5 = 22 - 5
0.25/0.25x = 17/0.25
x = <u>68</u> minutes