calculus

two trains are on parallel tracks that are 2 miles apart. If both trains are traveling at 40 mph, how fast is the distance between the trains decreasing when they are 8 miles apart?

  1. 👍 0
  2. 👎 0
  3. 👁 156
  1. Hmmm. They are coming toward each other , distance decreasing, and you want to know when the are 8 miles apart when they started 2 miles apart? Makes no sense.

    relative velocity=80mph
    that is how fast the distance between them is decreasing at any time. This problem is not thought out, or typed wrong. Perhaps it would make better sense if the word "parallel" were change to perpendicular, however, it is very difficult to start them at 2mi apart, move them toward a common point, and sometime later be 8 mi apart.

    1. 👍 0
    2. 👎 0
  2. The parallel tracks are 2 miles apart

    1. 👍 0
    2. 👎 0
  3. If one train is x miles from the point of closest approach, and the other is y, then

    dx/dt = dy/dt = -40

    the distance z between the trains is

    z^2 = (x+y)^2 + 2^2
    So, when they are 8 miles apart,
    (x+y)^2 + 4 = 64
    x+y = √60

    z dz/dt = (x+y)(dx/dt+dy/dt)
    8 dz/dt = √60(-40-40)
    dz/dt = -10√60
    = -77.5

    Sounds reasonable. If they were on the same track, they'd be approaching at 80 mph, so we'd expect the speed to be a little less than that.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    two metra trains are on separate but parallel tracks. One has a speed of 90 km/hr, the other 80 km/hr. Initially, the two trains are 2.71 km apart. How long will it take the two trains to pass each other?

  2. Algebra

    Two trains leave Raleigh at the same time, one traveling north, the other south. The first train travels at 50 miles per hour and second at 60 miles per hour. In how many hours will the trains be 275 miles apart?

  3. Math

    Two trains are both traveling at a constant speed toward each other on neighboring tracks. The trains are 252 miles apart when they start traveling. They pass each other 4 1/2 hours later. One of the trains is traveling 25 3/4

  4. physics

    Two trains face each other on adjacent tracks. They are initially at rest, and their front ends are 50 m apart. The train on the left accelerates rightward at 1.05 m/s2. The train on the right accelerates leftward at 0.93 m/s2.

  1. math

    Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 65 miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet?

  2. PHYSICS

    Two Metra trains approach each other on separate but parallel tracks. Train A has a speed of 90 km/ hr, train B has a speed of 80 km/ hr. Initially, the two trains are 2.71 km apart. How long will it take the two trains to meet?

  3. Math

    Two trains leave stations 216 miles apart at the same time and travel toward each other. one train travels at 95 miles per hour while the other travels at 85 miles per hour how long will it take for two trains to meet? Do not

  4. Physics

    As two trains move along a track, their conductors suddenly notice that they are headed toward each other. The figure below gives their velocities v as functions of time t as the conductors slow the trains. The slowing processes

  1. Math

    An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 12 miles per hour faster than the westbound train. After 1.5 hours, they are 174 miles apart.

  2. Physics

    Two trains face each other on adjacent tracks. They are initially at rest, and their front ends are 30 m apart. The train on the left accelerates rightward at 1.17 m/s^2. The train on the right accelerates leftward at 1.1 m/s^2.

  3. math

    2 trains going opposite directions leave at the same time. Train b is 10mph faster than train a. in 8 hours the trains are 960 miles apart. find the speed of each

  4. Physics - position time graph

    The graph shows position as a function of time for 2 trains running on parallel tracks. The graph shows line A at a 45 degree angle,beginning at origin. Curve B also begins at origin, continues up and to the right (all in quadrant

You can view more similar questions or ask a new question.