You are here:

Calculus/related rate

Advertisement


Question
A railroad bridge is 20 feet above a river. A baby is driving a train traveling 60mi/hr passes over the middle of the railroad bridge at the same instant that a puppy in a boat traveling 20 mi/hr passes under the middle of the bridge. Looking from the view of a satellite how fast are the baby and puppy moving away from each other 10 sec later?

Answer
Since a mile per hour is the same as 88 feet per minute,
divide by 60 again and get 22/15 feet per second.

This make 60 mi/hr into 88 f/s and 20 mi/hr into 44/5 ft/s.

After 10 sec, the train is 880 feet away from the bridge
and the ship is 44/3 feet away from the bridge.

If the train is t feet away and the boat is b feet away,
the distance d between them is found using tē + bē = dē.

Differentiating gives 2tt' + 2bb' = 2dd'.
Dividing by 2d gives (tt' + bb')/d = d'.

Using what I have said, t and b are the distances away, which were found at 10 sec,
t' and b' are the speeds, which were given, and
d is the distance, which can be found to be sqrt(tē + bē).

Calculus

All Answers


Answers by Expert:


Ask Experts

Volunteer


Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).

Experience

Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2016 About.com. All rights reserved.