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Word Problems

by Angela Valdez
(Deming, NM, USA)

I have a couple of word problems that I am having difficulty finding the equation to plug the numbers into. I would like to know the equation to solve the problems, please.

Stan's tractor is just as fast as James's. It takes Stan 1 hour more than it takes James to drive to town. If Stan is 20 miles from town and James is 15 miles from town, how long does it take James to drive to town?


To determine the number of trout in a lake, a conservationist catches 112 trout, tags them, and throws them back. Later, 82 trout are caught, 32 of them tagged. Estimate the number of trout in the lake.

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May 30, 2011
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Proportions
by: Anonymous

The easiest way to solve these problems is by using proportions.


Stan's tractor is just as fast as James's. It takes Stan 1 hour more than it takes James to drive to town. If Stan is 20 miles from town and James is 15 miles from town, how long does it take James to drive to town?


You must know the distance formula: d = rt
Since we need to find the rate, we can solve for r.

r = d/t.

We know the rate is the same for both tractors, so let's set the ratios equal to each other.

Stan's rate = James's rate
Let x = James's time
Let x+1 = Stan's time since it takes him an hour longer.

20/x+1 = 15/x

From here you must cross multiply to solve for x.

15(x+1) = 20x
15x+15 = 20x Distribute the 15
15x-15x +15 = 20x - 15x Subtract 15x
15 = 5x

15/5 = 5x/5 Divide by 5

3 = x

X = 3 hours for James's time, which means that Stan would take 4 hours.

The question asks for how long it takes James to drive to town, which would be 3 hours.

You know this is correct, because if we substitute back into the distance formula, we know that:
d = rt
15 = 5(3) The rate would have to be 5.

This works for Stan too
20 = 5(4) Since Stan's time would be 4 hours. The rate is the same.




To determine the number of trout in a lake, a conservationist catches 112 trout, tags them, and throws them back. Later, 82 trout are caught, 32 of them tagged. Estimate the number of trout in the lake.

We an set up a ratio with:
# of tagged trout/Total trout caught.

We know that 82 are caught and 32 are tagged, so...
32/82 would be the ratio.

We also know 112 are tagged, but we don't the total, so... 112/x

Let x = total trout estimated in lake.

Let's set up a proportion, with the ratios being equal

32/82 = 112/x

Cross multiply:
32x = 9184

32x/32 = 9184/32
x = 287

There are an estimated in 287 trout in the lake.

Let's check:
The ratio we know is: 32/82 which is 39% So about 39% of the total fish are tagged.

Let's check our answer: 112/287 = 39% So if 112 were tagged, that's 39% of the estimated total (287).

Hope this helps!

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