Word Problems

[MaryJane]

I am having to do these word problems, and don't have a clue where to start. I always come to a dead end.

Tara plans to take a bath, but forgets to close the drain. The bath usually takes 10 minutes to fill and 12 minutes to empty. How long will it be before the bath is filled if Tara continues not to notice that the drain is opened.
-- Ok, I know this has to do with writing equations and cancleing them out, I think.

A penguin swimming with the ocean current in search of food takes 1 hour to travle 9 miles. Its return trip upstream to its starting point takes it 3 hours. What is the penguin's speed in still water.
--Same thing goes.

I'd really appreciate the help.

 

[Mrspi]

I am having to do these word problems, and don't have a clue where to start. I always come to a dead end.

Tara plans to take a bath, but forgets to close the drain. The bath usually takes 10 minutes to fill and 12 minutes to empty. How long will it be before the bath is filled if Tara continues not to notice that the drain is opened.
-- Ok, I know this has to do with writing equations and cancleing them out, I think.

A penguin swimming with the ocean current in search of food takes 1 hour to travle 9 miles. Its return trip upstream to its starting point takes it 3 hours. What is the penguin's speed in still water.
--Same thing goes.

I'd really appreciate the help.

Problem 1:

If the bath can be filled in 10 minutes, then in each minute, 1/10 of the tub is filled.

If the bath can be emptied in 12 minutes, then in each minute, 1/12 of the tub is emptied.

If both the faucet and the drain are going, in 1 minute you would fill (1/10 - 1/12) of the tub.

Now, suppose it takes x minutes for Tara to fill the tub. That means that
x(1/10 - 1/12) = 1
where 1 represents the full tub.

Can you solve it now?

For the second problem,
let s = penguin's speed in still water
let c = speed of current

traveling with the current, the penguin's speed will be s + c mph, and it can travel 9 miles in 1 hour. Remember that distance = rate * time.

So, traveling WITH the current,
9 = 1(s + c)

Traveling against the current, the penguin's speed will be s - c mph. It takes the penguin 3 hours to travel 9 miles. So,
9 = 3(s - c)

You have two equations in two variables:
9 = s + c
9 = 3(s - c)

You should be able to solve it now.