SOLUTION: A ship that is in danger of sinking radios the coast Guard for assistance. When the rescue craft leaves the Coast Guard station, the ship is 60 miles away and heading directly towa

Question 1125908: A ship that is in danger of sinking radios the coast Guard for assistance. When the rescue craft leaves the Coast Guard station, the ship is 60 miles away and heading directly toward the station. If the average speed of the ship is 10 miles per hour and the average speed of the rescue craft is 20 miles per hour, how long will it take for the rescue craft to reach the ship?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
ship is traveling at 10 miles per hour and the rescue craft is traveling at 20 miles per hour.

ship is 60 miles away and heading directly toward the station.

rate * time = distance.

ship is traveling 10 miles per hour for T hours for a distance of D miles.

rescue ship is traveling 20 miles per hour for T hours for a distance of 65 - D miles.

formula for ship is 10 * T = D
formula for rescue ship is 20 * T = 65 - D

these are 2 equaitons that need to be solved simultaneously.

various ways to do so.
substitution is one of them.
since D = 10 * T from the first equation, replace T with that in the second equation to get :
20 * T = 65 - 10 * T
add 10 * T to both sides of the equation to get 30 * T = 65
divide both sides of the equation by 30 to get T = 65/30 = 13/6.
they will meet when T = 13/6 hours.

ship will travel 10 * 13/6 = 65/3 miles = 21 and 2/3 miles.
rescue will travel 20 * 13/6 = 130/3 miles = 43 and 1/3 miles.
total distance traveled by both ships = 65 miles.

solution looks good.

solution is that the rescue ship will take 13/6 = 2 and 1/6 hours to meet the ship in distress.

RELATED QUESTIONS
Rescue at Sea: A ship that is in danger of sinking radios the coast Guard for... (answered by chessace)

: a sailboat is taking on water during a storm and is in danger of sinking. after calling (answered by josgarithmetic)

A lighthouse and Coast Guard rescue boat are located 25 miles apart. One evening, the... (answered by ikleyn)

A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a (answered by ikleyn)

1. A search plane has a cruising speed of 250 miles per hour and carries enough fuel for... (answered by ikleyn)

1: stephanie leaves school at 3:00 on her bike and travels at a speed of 10mph. if her... (answered by TimothyLamb)

Two coast guard ships, the Alpha and the Beta, are 3000ft apart. The angles from a line... (answered by stanbon)

Two coast guard ships, the Alpha and the Beta, are 3000ft apart. The angles from a line... (answered by greenestamps)

Two coast guard ships, the Alpha and the Beta, are 3000ft apart. The angles from a line... (answered by josgarithmetic)