Question

A passenger ship and an oil tanker left port sometime in the morning; the former headed north, and the latter headed east. At noon the passenger ship was 40 mi from port and moving at 30 mph, while the oil tanker was 30 mi from port and moving at 20 mph. How fast was the distance between the two ships changing at that time

Answer 1

Answer:

distance between the two ships changing at that time is 36 mph

Step-by-step explanation:

given data

ship = 40 mi from port

ship moving = 30 mph

oil tanker = 30 mi from port

oil tanker moving = 20 mph

solution

we will apply here pythagoras theorem so we get here

x² + y² = L²   .....................1

here x is distance of ship from port

and y is distance of oil tanker from port

and L is distance between oil tanker and ship

so put here value and we get

40² + 30² = L²

L = 50 mile

now we differentiate equation1 with respect to time t

$2x\ \frac{dx}{dt} + 2y\ \frac{dy}{dt} = 2L\ \frac{dL}{dt}$      ...............2

put here value  and we get

40 × 30 + 30 × 20 = 50 × $\frac{dL}{dt}$  

$\frac{dL}{dt}$   = 36 mph

so distance between the two ships changing at that time is 36 mph