# Word Problem Involving Time,Distance and Linear Equations???

#### dfunk

##### New member
Hi,

My homeschooled son is stuck on a few problems and I'm hoping that you can help me help him. Here are the problems, can someone explain to me the logic/forumula behind them? Answers are in parenthesis, however we need help understanding how they got to the answer.

You are going on a trip to the Natural History Museum. AT 9am you leave for the museum, which is 120 miles away. At 10:15 you are 63 miles away from the museum.
:: Write a linear equation that gives the distance d (in miles) from teh museum in terms of the time t. Let t represent the number of minutes since 9. (d= -0.76t = 120)
:: Find the distance you are from the museum after you have traveled 2 hours. (28.8 mi)
:: According to your equation, when will you reach the museum? at about 11:38 AM

A mountain climber is scaling a 300 foot cliff at a constant rate. The climber starts at the bottom at noon and by 12:300 the climber has moved 62 feet up the cliff.
:: Wrie an equation that gives the distance d (in feet) remaining in teh climb in terms of the time t (in hours). What is the slope of the line? (d = -124t + 300)
:: At what time will the mountain climber reach the top of the cliff? (at about 2:25 pm)

Thank you for any help that you can provide.

#### stapel

##### Super Moderator
Staff member
dfunk said:
My...son is stuck on a few problems and I'm hoping that you can help me help him.
Certainly, we can help! Please have your son reply (or dictate a reply) showing everything he has tried so far, so we know where he is having trouble. Please ask him to be sure to be complete. Thank you! :wink:

Eliz.

#### Subhotosh Khan

##### Super Moderator
Staff member
dfunk said:
Hi,

My homeschooled son is stuck on a few problems and I'm hoping that you can help me help him. Here are the problems, can someone explain to me the logic/forumula behind them? Answers are in parenthesis, however we need help understanding how they got to the answer.

You are going on a trip to the Natural History Museum. AT 9am you leave for the museum, which is 120 miles away. At 10:15 you are 63 miles away from the museum.

First thing , for this problem, that needs to be done is to find your speed

To do that, you'll use the equation:

speed = (distance)/(time)

:: Write a linear equation that gives the distance d (in miles) from teh museum in terms of the time t. Let t represent the number of minutes since 9. (d= -0.76t = 120)
:: Find the distance you are from the museum after you have traveled 2 hours. (28.8 mi)
:: According to your equation, when will you reach the museum? at about 11:38 AM

A mountain climber is scaling a 300 foot cliff at a constant rate. The climber starts at the bottom at noon and by 12:300 the climber has moved 62 feet up the cliff.
:: Wrie an equation that gives the distance d (in feet) remaining in teh climb in terms of the time t (in hours). What is the slope of the line? (d = -124t + 300)
:: At what time will the mountain climber reach the top of the cliff? (at about 2:25 pm)

Thank you for any help that you can provide.

#### dfunk

##### New member
We are having trouble with the entire thing - don't know where to start.

What he has done is this:

He got the speed dividing distance by time, which was 57 miles divided 75 minutes = .76 miles/minute

He can't seem to explain anything beyond that. The problem I have with him is that he just does stuff in his head and I can't get him to show me the work. He is only 11 and is actually quite bright in math and I keep telling him he has to show me his work but he gets very frustrated with that. I was the same way as a kid - math came easy and it was all automatic calculations in my head - I aced it through geometry, but then when I got to trig and calculus I floundered. (and now, 25 years later, i've forgotten most of what I leared) I keep trying to tell him how important it is to show work but he fights me.

#### stapel

##### Super Moderator
Staff member
dfunk said:
We are having trouble with the entire thing - don't know where to start.
Ah; so your curriculum didn't cover "uniform rate" word problems. (Otherwise, you'd have the basic equation, plus lots of worked examples.)

Since we cannot replicate the missing section, you will need to consider hiring a qualified local tutor, or else try self-study through online lessons. If you would like to attempt the latter, there are many great lessons, complete with worked examples, available online:

. . . . .Google results for "distance rate time word problems"

Have fun! Eliz.

#### kasie-tutor

##### Banned
Dear dfunk,

A "linear equation" is an equation that is a straight line. Have you seen this?: $$\displaystyle y=mx+b$$

In this equation you have to find m, or the rise over run, and b, the y-intercept.

Find the Rise and Run

Draw a picture. An "L" shaped graph with "minutes since 9am" on the x-axis and "distance from museum" on the y-axis.

Plot your two given coordinates (points). One of the points is (0, 120). Can you figure out the other one?

Connect the two points, then form a right triangle with that line as the hypotenuse (diagonal side).

The Rise is the vertical leg of the triangle; the Run is the horizontal leg.

Find the Y-Intercept (b)

Look at your picture. The y-intercept is the coordinate where the line intercepts the y-axis. "b" is the y-coordinate of the y-intercept. (i.e., if it crossed at (0, 100), b would be 100).

Now write your equation

y = (put the ratio of your rise over run)x + (put what b is)

So you have a linear equation in the form of y = mx + b.

Optional

You could use the letter "D" instead of "y" so that it stands for "Distance" and the letter "t" for "time" instead of "x".

Note

This way of getting the equation by drawing a picture won't always be the best way. You might need more help when you can't get an accurate answer from a graph. Since your son is only 11, I was assuming he isn't expected to solve it as "mathematically" as much as "by using a picture".

I hope that gets you started. If you look in your books index for more information, look up "linear equation".