Two hoses together fill a pool in 2 h. If only hose A is used, the pool fills in 3 h. How long would it take to fill the pool if only hose B were used?
I multiplied 3 and 2 and got 6 hours.
Is this a valid method?
Thanks
nope. consider the fraction of the job done in one hour:
1/3 + 1/b = 1/2
In this case you got lucky, since indeed 1/3 + 1/6 = 1/2.
Thanks!
No, multiplying the times from the given information is not a valid method in this case. Let's reason it out step by step to find a correct solution:
Let's say hose A fills 1/3 of the pool in 1 hour (since the pool fills in 3 hours with only hose A being used). Similarly, hose A and B together fill 1/2 of the pool in 1 hour (since the pool fills in 2 hours with both hoses being used).
Now, let's find out how much of the pool hose B fills in 1 hour when used alone. Let's denote the amount of pool filled by hose B alone in 1 hour as 1/x, where x is the time taken by hose B alone to fill the pool.
From the given information, we know that:
- Hose A fills 1/3 of the pool in 1 hour: A = 1/3
- Hose A and B together fill 1/2 of the pool in 1 hour: A + B = 1/2
Since the total pool is 1, we can set up the equation:
A + B = 1/2
Substituting the value of A, we have:
1/3 + B = 1/2
To solve for B, we need to isolate it on one side of the equation:
B = 1/2 - 1/3
B = 3/6 - 2/6
B = 1/6
So, hose B fills 1/6 of the pool in 1 hour.
Now that we know the rate at which hose B fills the pool, we can find the time it takes to fill the entire pool using hose B alone. Since hose B fills 1/6 of the pool in 1 hour, it will take 6 hours to fill the whole pool.
Therefore, the correct answer is 6 hours, not 2 hours as you initially calculated by multiplying the times.