Question

How do you get better at word problems? In Geometry I did well. However, algebra word problems are usually hard for me to figure out. Any tips?

Answer 1

What type of word problems do you have a hard time with?

It may not sound like great advice, but practice helps... after awhile, you start seeing how to "translate" the words into algebra thoughts.

Answer 2

Do you have an example of one that gives you trouble?

Answer 3

An aircraft carrier left the Dania Pier and traveled toward Guam. 0.2 hours later a container ship left traveling 0.2 mph faster in an effort to catch up to it. After 13.8 hours the container ship finally caught up. What was the aircraft carrier's average speed?

Answer 4

Another thing I do is read the problem a bunch of times... I don't usually pick up on all the details the first time through, so it takes a couple of re-reads... I look for ideas that can be variables, and see whether the problem gives me the value of the variable or if it is not yet known.

Simple example: Steve is 5 years older than Bob. Bob is 7 years old. How old is Steve?

So I would read the problem and say, hmmm... I could make a variable "S" for Steve's age, and a variable "B" for Bob's age.

Then I would say... the problem tells me that Bob is 7, so I can write "B = 7".
But it doesn't tell me how old Steve is, so I don't know S... I need to solve for S.

And then I try to use the problem to write an equation for the thing I don't know, like Steve's age...

So I would start with that unknown "S" on the left side, and then on the right side, I would try to write the math sentence that matches with "5 years older than Bob".

S = B + 5

Then I could use the fact that Bob is 7... B = 7.... to substitute 7 for B in that equation, allowing me to add and find that S = 12, which means Steve is 12 years old.

That's an easy example, but the process is similar for any word problem... just keep going through looking the problem's wording and try to write the parts as math. Then look for ways to use the information given to find the unknown.

After you do lots of them, you sort of start to see the pattern of how words match up with math equations, but it just takes practice.

Answer 5

Ok, so let's do the process with your problem:

An aircraft carrier left the Dania Pier and traveled toward Guam. 0.2 hours later a container ship left traveling 0.2 mph faster in an effort to catch up to it. After 13.8 hours the container ship finally caught up. What was the aircraft carrier's average speed?

Answer 6

Sorry, let's be more specific with the variables...

Aircraft carrier:
Call its speed "v_a" (like "velocity of aircraft carrier")
and its distance "d_a"

Container ship: speed is v_c and distance is d_c

And you know that the container ship is 0.2 miles per hour faster than the carrier, so you also know v_c = v_a + 0.2

Answer 7

So the distance the aircraft carrier has traveled after some amount of time we can call "t" hours is its speed multiplied by that time "t".

d_a = v_a * t

And the distance the container ship has traveled is similar, but you have to subtract 0.2 hours from the time, since it started later.

d_c = v_c * (t - 0.2)

Answer 8

You then know that after 13.8 hours, the distance traveled by both ships is the same, since the problem says that's when the container ship caught up...

When t = 13.8, then d_a = d_c

So you want to use the full expression for d_a and d_c and sub in t = 13.8

d_a = v_a * t --->>> d_a = v_a * 13.8
d_c = v_c * (t - 0.2) --->>> d_c = v_c * (13.8 - 0.2)

And then set those 2 expressions to be equal each other:
d_a = d_c
13.8* v_a = v_c * (13.8 - 0.2)

Finally, you can use the fact that you know the container ship is 0.2 mph faster than the aircraft carrier.... v_c = v_a + 0.2 to get rid of the v_c term in that last equation...

13.8* v_a = (v_a +0.2) * (13.8 - 0.2)

Answer 9

Then, finally, you can solve for the aircraft carrier's speed, v_a in that last equation.

Answer 10

This was a complicated word problem though :) I understand why you might have had trouble with it!!!

Answer 11

So, to review:

Start by naming the variables. Next, look for relationships between the variables, like the fact that one speed was just 0.2 more than the other.

Next, you need to realize any "hidden" clues, such as that the distance of each ship would be equal when the container ship catches up... that "equal" is your big clue... that means you can set up that equation saying distance 1 = distance 2. Then using the variables and relationships between them, you can sub in and solve.

It's not easy, but with practice, you can sort of see the pattern in how the problems work. But the big thing I find is that I just need to keep thinking "what else can I do here?" Lots of times I cannot see the whole strategy at the beginning... I have to just start writing stuff down as math expressions, and then thinking "ok, what's next?"

Answer 12

I wish it were as easy as just telling you "oh, just do it like this", but it's really just a matter of practicing the process on lots of different types of problems.