Hendrik is going on a hike. If he can cover 2 miles in an hour, how many hours will it take him to hike 5 1/4 miles?

Answer 1

Word problems. The dreaded type of problem most students loathe. Don't fall for that trap. I have 4 steps you can use in every word problem you'll ever face. Follow these steps and word problems will be least of your worries.

Step 1: READ

First thing with any word problem. READ IT. Don't just skim it. READ IT. Understand what's going on and what's you being asked to find. This step is crucial to setting up your equations. The most common mistake students make is randomly putting numbers they skimmed in the wrong places simply because they didn't understand what those numbers mean.

Ok, so we've read the problem. We understand that Hendrick is going for a hike. We also know he can walk 2 miles per hour. We are being asked how long will it take Hendrick to hike 5 1/4 miles.

Step 2: DEFINE YOUR VARIABLE(S)

This is going to seem backwards, but define your variable before picking a variable. WHAAAAAT!? I know, but stay with me. The question that usually appears at the end of the problem is your definition. In this case, our definition is: number of hours it will take Hendrick to hike 5 1/4 miles. Now what variable to use? You can use x; however, I have found it easier to pick a variable that closely represents the question. We are looking for hours, so use h. So, we have:

h = number of hours it will take Hendrick to hike 5 1/4 miles

Step 3: CREATE YOUR ALGEBRAIC EQUATION

We are now going to re-read the problem word for word, converting what we read into algebraic expressions that will become an algebraic equation by the time we finish re-reading.

First we read that "Hendrick is going for a hike." This sentence has nothing for us to convert. It's what we call a filler sentence. You'll know it's a filler sentence when there is no mention of anything numeric.

Moving on. "if he can cover 2 miles in an hour" That's a rate, so we're multiplying. We see the 2, but what are we multiplying to it? Our unknown variable h. Whoohoo. We now have:

2h representing how far he hikes in h hours at a rate of 2 miles per hour

"how many hours will it take him to hike 5 1/4 miles?" 2h represents how far he hikes in h hours, 5 1/4 miles is how far he hikes, so set these two equal to each other.

2h = 5 1/4 I personally dislike mixed fractions. They're messy and can get hard to read.

2h = 5.25 There, that's better.

Step 4: SOLVE YOUR EQUATION (and write out your answer)

h = 2.625

This would be a sufficient answer if it started out as a basic equation solving for the variable. This isn't the situation here. I'm a firm believer if the problem started with words, it has to end with words. We were asked how many hours it would take Hendrick to hike 5 1/4 miles. Saying h = 2.625 wouldn't make any sense would it? Neither would saying 2.625 hours. Who talks that way? Do you know how to convert this decimal to actual time? Multiply everything to the right of the decimal point by 60 (as in 60 minutes to an hour). We get 37.5. Final answer:

It will take Hendrick about 2 hours and 37 minutes to hike 5 1/4 miles.

RECAP

Step 1: READ THE PROBLEM

Step 2: DEFINE YOUR VARIABLE

h = number of hours it will take Hendrick to hike 5 1/4 miles

Step 3: CREATE YOUR EQUATION(S)

2h = 5.25

Step 4: SOLVE YOUR EQUATION (and write out your answer)

h = 2.625

It will take Hendrick about 2 hours and 37 minutes to hike 5 1/4 miles.