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
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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?
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.
