Help me with an Algebra 1 problem (from LOF)

[Cindyg]

Sergeant Snow stopped for doughnuts. The main convoy continued on at 45 mph while Sergeant Snow was in the doughnut shop for one hour. After the hour, Sergeant Snow got back in his van and continued his trip at 60 mph. How long before Snow catches up to the convoy?

 

Here's my wrong answer: (Tell me why I'm wrong.)

 

1st hour: Snow goes 0 miles, convoy goes 45 miles.

2nd hour: Snow goes 60, convoy has gone 90

3rd hour: Snow has gone 120, convoy has gone 135

4th hour: Snow has gone 180, convoy has gone 180.

 

Answer: 4 hours.

 

Here's the author's answer:

 

Let t = the number of hours till Snow catches the convoy.

 

Then 60t = the distance from the doughnut store to the point where he catches up to the convoy.

 

Then 45(t+1) is the distance from the doughnut store that the convoy drives until it is overtaken by snow.

 

60t=45(t+1)

60t=45t+45 (distributive law is the point of the lesson)

15t=45

t=3 hours

 

Where did I go wrong?

Edited January 31, 2012 by Cindyg

[regentrude]

If I read this correctly, you are just counting differently: you count from when Snow goes to hang out in the donut shop and the convoy starts. THEY count from when Snow actually gets moving (Their variable t counts the time Snow is on the road; t+1 is the time the convoy is moving)

YOUR time is the total time. So, you have the same answer.

 

I would encourage you to understand how they set it up with the system of equations; your procedure of comparing distances for each at full hours will get you the answer easily only if the time is in whole hours, but not in fractions of hours.

[JeanM]

Sergeant Snow stopped for doughnuts. The main convoy continued on at 45 mph while Sergeant Snow was in the doughnut shop for one hour. After the hour, Sergeant Snow got back in his van and continued his trip at 60 mph. How long before Snow catches up to the convoy?

 

Here's my wrong answer: (Tell me why I'm wrong.)

 

1st hour: Snow goes 0 miles, convoy goes 45 miles.

2nd hour: Snow goes 60, convoy has gone 90

3rd hour: Snow has gone 120, convoy has gone 135

4th hour: Snow has gone 180, convoy has gone 180.

 

Answer: 4 hours.

 

Here's the author's answer:

 

Let t = the number of hours till Snow catches the convoy.

 

Then 60t = the distance from the doughnut store to the point where he catches up to the convoy.

 

Then 45(t+1) is the distance from the doughnut store that the convoy drives until it is overtaken by snow.

 

60t=45(t+1)

60t=45t+45 (distributive law is the point of the lesson)

15t=45

t=3 hours

 

Where did I go wrong?

 

The t in your solution and the t in the author's solution are different. Your t is the time beginning when Snow stopped for doughnuts (including the 1 hour in the store). The author's t is the time it takes Snow to actually travel the distance (not including the time in the store).

 

So you are both correct. Does that help?

[wapiti]

It is in the wording of the question, which is a little vague - how long from when he stopped for doughnuts or how long from the time he started driving again.

[Cindyg]

Oh, thank you guys! I could not figure out why my answer would be wrong! I feel much better.

 

:)

[kiana]

I would encourage you to understand how they set it up with the system of equations; your procedure of comparing distances for each at full hours will get you the answer easily only if the time is in whole hours, but not in fractions of hours.

 

100% agree. They give you problems that you can solve another way at first, so that you can check your answers easily and the numbers are small -- but you should practice the procedure as well.

[Sweet Charlotte]

I have been thru that section twice now, and I have been confused both times. This last time I even emailed the author to get him to explain it to me. I love Fred, but I think my brain works differently than his...

Edited January 31, 2012 by Sweet Charlotte
Typo

[wapiti]

I have been thru that section twice now, and I have been confused both times. This last time I even emailed the author to get him to explain it to me. I love Fred, but I think my brain works differently than his...

Here's a video on speed problems that might help: Speed Part 2

Edited February 1, 2012 by wapiti

[EKS]

It's three hours after Snow starts. It doesn't include the time he was in the donut shop.

[Cindyg]

100% agree. They give you problems that you can solve another way at first, so that you can check your answers easily and the numbers are small -- but you should practice the procedure as well.

 

Point taken.

 

Here's a video on speed problems that might help: Speed Part 2

 

Wapiti, could you try your link again? It did not work.

[wapiti]

Wapiti, could you try your link again? It did not work.

 

oops - sorry! fixed it Speed Part 2 He solves the following problems in this video:

 

 

A tortoise and a hare have a 400 ft race. The tortoise crawls 5 ft per minute the entire time. The hare runs the first half of the distance at 200 ft per minute, and walks the rest at 2 ft per minute. Who wins?

 

A tortoise and a hare have a 400 ft race. The tortoise crawls 5 ft per minute the entire time. The hare runs the first half of the distance at 200 ft per minute, and walks the rest at 2 ft per minute. How many minutes after the start does the tortoise catch the hare?

Edited February 1, 2012 by wapiti