GED Math: Distance, Rate, and Time

Yo, all you GED studiers. Zaher wrote me with a good math problem… ’bout distance and speed and time. Take a gander…

Hey Curtis ,

Thanks for your prompt reply man . This is one of the problems I struggled with involving distance :

– A man started walking at 2 mph, while a woman 2 miles behind him began walking at the same time at a rate of 4 mph, and in the same direction. Just then, the man’s dog left him and ran toward the woman. Upon reaching her, it instantly turned around and ran back toward thr man. And so, the dog continued to run back and forth between them, at a constant rate of 5 mph, until the woman finally overtook the man. How far did the dog run?

**** Go enjoy figuring it out and let me know how to do it man !


In the GED test, on the page with all the formulas, you got one for distance:

distance = rate x time

So, what’s it mean? Distance is how far you gonna go, rate is how fast you goin’, and time is, well, time. So, how far you go is how fast you go times how long you’re travelin’. In other words, if you get in your car and start drivin’ down the highway, the faster you go, and the longer time you drive, the farther you’ll get. Makes sense, right? If your speed (rate) goes up, the distance you travel goes up. If your time (how long you drive) goes up, the distance you travel goes up.

How does it get applied to the problem? This problem is tough, not because the math is tough, but because it’s tough to figure out how to use the math to solve it. You gotta take it one step at a time and figgure out what’s really goin on here.

Okay, we got a guy walkin’. Same idea as driving, how far = how fast x time. And, we got a woman walking, to. So that’s complicatin’ it up. We got to deal with 2 people walkin’ at once. And a dog, runnin’ back an fo’! Okay, problem with this problem is it’s hard to see. What’s the real question? How far’s the dog go? How do I figure that out?

Hey, this is harder than anythin’ on the GED. So, let’s stretch our minds. To get my mind around it, sketchin’ a picture sometimes helps. Scuse my bad drawin’.

So, the real point is, how far does the dog go? We want to know distance (how far), which is rate times time:

dog distance = rate x time

dog distance = 5 mph x time

Okay, to answer the question, we run into another question… how long does the dog run? He runs from the time they start walkin’ until the two people meet. Now, we gotta answer a second question to answer the first. How long does it take the woman to get to the guy?

We’re usin’ the same formula, an’ tryin’ to find the time it takes for the woman to catch up.

distance = rate x catchup time

The distance they start out is 2 miles:

2 miles = rate x catchup time

What’s the rate? The man is walking at 2 mph, and the woman is walking at 4 mph. She’s catching up to him, but how fast? For every 4 mph she walks, you’ve gotta subtract the 2 mph he’s walked in the same direction during that same time. So, she’s gaining 2 mph on him.

2 miles = (4 mph – 2 mph) x catchup time

2 miles = 2 mph x catchup time

Now, it’s just math. divide each side by 2, and you get:

1 hour = catchup time

How do you know the units are hours? It’s 1 hour, because we’re talkin’ miles and miles per hour. So, one question solved! Now we take the answer and go back to our original question:

dog distance = 5 mph x 1 hour

dog distance = 5 miles

Whew! Dat dog goin’ doggone fast!

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