# Calculus

at 12 noon ship A is 65 km due north of a second ship B. Ship A sails south at a rate of 14km/hr, and ship B sails west at a rate of 16km/hr. How fast are the two ships approaching each other 1.5 hours later at 1:30pm? Thank You!

1. Making a sketch for the 12 noon position, placing B at the origin and A 65 units up on the y-axis
At a time of t hrs after noon,
let the distance covered by A be 14t
let the distance covered by B be 16t
Draw a line between their positions and call it d km

d^2 = (16t)^2 + (65-14t)^2
when t = 1.5
d^2 = 620
d = √620

2d dd/dt = 2(16t)(16) + 2(65- 14t)(14)
dd/dt = (256t + 65 - 196t)/√620
when t=1.5
dd/dt = (256(1.5) + 65 - 196(1.5))/√620
= 6.22 km/h

check my arithmetic

posted by Reiny

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