1. ## Ratio

Can you guys help me answer this question? It's been far too long since I've done ratios.

"Drain A will empty a tank in 5 hours. Drain B will empty the tank in 6 hours. How long will it take to empty the tank using both drains?"

And

"30 min : q min = 6 days : 2 weeks"

2. Let t be the number of hours needed for A and B to drain the tank.

1/5=part drained by A in 1 hr.

1/6=part drained by B in 1 hr.

1/t=part drained by both in 1 hr.

1/5+1/6=1/t, solve for t

3. Hmm... but they don't drain a part of the tank. They drain the whole tank in 5 or 6 hours.

4. Originally Posted by Rocher
Can you guys help me answer this question? It's been far too long since I've done ratios....
And

"30 min : q min = 6 days : 2 weeks"
Hello, Rocher,

rewrite this proportion:

$\frac{30\text{ min}}{q\text{ min}}=\frac{6\text{ days}}{14\text{ days}}$. The units cancel out.
Multiply by q and by 14 and you'll get:

$30 \cdot 14=6 \cdot q$. Solve for q

(For confirmation only: 70)

EB

5. Ty!! I just need help on the first question now :P

6. Originally Posted by Rocher
...

"Drain A will empty a tank in 5 hours. Drain B will empty the tank in 6 hours. How long will it take to empty the tank using both drains?"
...
Hell, Rocher,

galactus has demonstrated what you should calculate. I'll add a few steps so it could be easier for you to understand:

1. contents of the tank: T
2. part of the content which is drained by A in 1 hour: 1/5*T
3. part of the content which is drained by B in 1 hour: 1/6*T

4. part of the content which is drained by A and by B together in 1 hour: 1/5*T + 1/6*T

5. Both pipes need t hours to drain the tank completly:

$t \cdot \left(\frac{1}{5} \cdot T+\frac{1}{6} \cdot T \right) = T$. simplify the LHS:

$t \cdot \frac{11}{30} \cdot T = T$. Divide by T and then solve for t:
$t=\frac{30}{11}\text{ h}\approx 2.72\ h$

To be exact the time is: 2 h; 43 min; 38.18 s

EB

7. You own =) I'm done my homework!! :P