# Calculus

At 2:00PM boat X is heading due west at 15mph towards a dock that is exactly 15 miles away. At the same time boat Y leaves the dock traveling due north at a speed of 20mph. At what time will the boats be closest together?

1. 👍 0
2. 👎 0
3. 👁 175
1. Let the time passed since the northbound ship left the dock be t hrs
Make a sketch
Distance traveled by northbound boat is 20t
distance from dock of westbound boat is 15-15t.
let the distance between them be D
D^2 = (20t)^2 + (15-15t)^2
= 400t^2 + 225 - 450t + 225t^2
= 625t^2 - 450t + 225
2D dD/dt = 1250t - 450
dD/dt = (625t - 225)/d
= 0 for a max/min of D
625t = 225
t = 225/625 = .36

so the time is .36 hours past 2:00 pm
.36 hrs = 21.6 minutes or 21 minutes 36 seconds

time is 2:21:36 PM

1. 👍 0
2. 👎 0
posted by Reiny
2. THANK YOU! I get it now!

1. 👍 0
2. 👎 0
posted by Allison

## Similar Questions

1. ### Calculus

a boat leaves a doct at 2:00pm, heading west at 15km/h. Another boat heads south at 12km/h and reaches the same dock at 3:00pm. When were the boats closest to each other.

asked by Tasmina on October 19, 2010
2. ### math

a boat leaves a dock at 2:00pm ,heading west at 15 km/h. another boat heads south at 12km/hand reaches the same dock at 3:00 pm, when were the boats were closest to each other.? tanks it will be help full if its explained well .

asked by khan on April 20, 2013
3. ### calculus

Boat A leaves the dock at 12pm heading due South at a constant speed of 20 km/h. Meanwhile, at 12pm Boat B, a pirate ship, is 15 km due West of the dock where boat A started, and is sailing due East at a constant speed of 15 km/h.

asked by Anya on November 10, 2010
4. ### Pre-calc

Boat A leaves a dock headed due east at 1:00PM traveling at a speed of 13 mi/hr. At 2:00PM, Boat B leaves the same dock traveling due north at a speed of 20 mi/hr. Find an equation that represents the distance d in miles between

asked by Emily on January 28, 2016
5. ### calculus

a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together

asked by LALA on November 14, 2011
6. ### Calculus (math)

A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 15 km/h. Another boat has been heading due east at 20 km/h and reaches the same dock at 3:00 P.M. How many minutes past 2:00 P.M. were the boats closest

asked by Olivia on November 8, 2014
7. ### Calculus (math)

A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 15 km/h. Another boat has been heading due east at 20 km/h and reaches the same dock at 3:00 P.M. How many minutes past 2:00 P.M. were the boats closest

asked by mariel on November 7, 2014
8. ### calc

A boat leaves a dock at 3:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 4:00 PM. How many minutes after 3:00 PM were the two boats closest

asked by sara on April 14, 2015
9. ### math

A boat pilot wishes to go in a straight line across a river from the east dock to the west dock in a ferryboat that has a still water speed 8.0 knots. If the river has a Southward current of 2.5 knots, what compass heading should

asked by b0b on November 3, 2015
10. ### Math

A boat pilot wishes to go in a straight line across a river from the east dock to the west dock in a ferryboat that has a still water speed 8.0 knots. If the river has a Southward current of 2.5 knots, what compass heading should

asked by Jack on November 3, 2015

More Similar Questions