Question

6. A train travels west toward St. Louis at 120 mph while a second train travels north from St. Louis at 90 mph. (a) At the instant when the first train is 10 miles east of St. Louis and the second train 20 miles north of St. Louis, how fast is the distance between the trains changing. (b) How fast is the distance between the trains changing 10 minutes later.

          6. A train travels west toward St. Louis at 120 mph while a second train travels north from St. Louis at 90 mph. (a) At the instant when the first train is 10 miles east of St. Louis and the second train 20 miles north of St. Louis, how fast is the distance between the trains changing. (b) How fast is the distance between the trains changing 10 minutes later.
        
Show more…
6. A train travels west toward St. Louis at 120 mph while a second train travels north from St. Louis at 90 mph. (a) At the instant when the first train is 10 miles east of St. Louis and the second train 20 miles north of St. Louis, how fast is the distance between the trains changing. (b) How fast is the distance between the trains changing 10 minutes later.

Added by Kevin B.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
please dont skip any steps, be neat :) 6.A train travels west toward St.Louis at 120 mph while a second train travels north from St. Louis at 90 mph. (a) At the instant when the first train is 10 miles east of St. Louis and the second train 20 miles north of St. Louis, how fast is the distance between the trains changing. (b)How fast is the distance between the trains changing 10 minutes later.
Close icon
Play audio
Feedback
Powered by NumerAI
Jennifer Stoner David Collins
Danielle Fairburn verified

Gregory Higby and 61 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
one-train-travels-west-toward-denver-at-120-mph-while-a-second-train-travels-at-90-mph-see-figure-below-north-away-from-denver-at-a-certain-moment-the-first-train-is-22-miles-east-and-the-se-24865

One train travels west toward Denver at 120 mph, while a second train travels north away from Denver at 90 mph (see Figure below). At a certain moment, the first train is 22 miles east and the second train is 58.5 miles north of the Denver station. Calculate the rate at which the distance between the trains is changing at that moment. Answer: The distance between the trains is changing at a rate of ___ mph.

Gregory H.

train-s-50-miles-north-of-a-train-station-is-traveling-towards-the-station-at-80-mph-train-w-is-20-miles-west-of-the-station-and-is-traveling-west-at-3015-miles-per-hour-from-the-station-how-fast-is-t

train s, 50 miles north of a train station is traveling towards the station at 80 mph. Train w, is 20 miles west of the station and is traveling west at 30.15 miles per hour from the station. How fast is the distance between the two trains changing at that instance

Dominique Jan T.

one-train-goes-west-at-a-rate-of-10-mph-and-another-train-goes-north-at-a-rate-of-20-mph-if-the-trains-started-in-the-same-place-how-fast-is-the-distance-between-the-trains-increasing-after-55629

One train goes west at a rate of 10-mph, and another train goes north at a rate of 20-mph. If the trains started in the same place, how fast is the distance between the trains increasing after 30 minutes?

Darshan M.


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,455 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,608 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,963 solutions

*

Transcript

-
00:01 All right, to start this problem, i'm just going to set up a formula.
00:04 We have x, y, and l.
00:07 And because we have a right angle in here, my formula is x squared plus y squared equals l squared.
00:14 And so they even tell you that i'm assuming the first train is the one that's on the right side.
00:22 So that's x equals 22.
00:25 And the one that's north is 58 .5.
00:32 That i want to find the distance between the two of them, and i'm just doing the pythagorean theorem, and i'm using a calculator because i don't even know what 58 .5 squared is.
00:43 And when i add it to the 22 squared, i get 3906 .25, but then i have to square root to cancel off the square.
00:53 So if i try to square root it, oh, it actually gives me a really nice answer of 62 .5.
00:59 I was not expecting that.
01:02 58 .5 here.
01:04 So what we also know is dxdt because this person is traveling west.
01:11 So it is a negative because this value is getting smaller.
01:16 120.
01:19 Whereas d ydt is going away.
01:26 I'm just double checking...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever