SOLUTION: A ship leaves the harbour and sails at 25 km/h. Another ship leaves 45 minutes later and sails in the same direction at 28 km/h. After how long will the second ship over take the f

Question 1136625: A ship leaves the harbour and sails at 25 km/h. Another ship leaves 45 minutes later and sails in the same direction at 28 km/h. After how long will the second ship over take the first?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.

the second ship will overtake the first ship when the distance both have traveled is the same.

the first ship will have traveled 45 minutes more than the second ship.

the equation for the first ship is:

25 * (time + .75) = distance.

this is because the first ship is traveling 45 minutes more than the second ship and 45 minutes / 60 = .75 hours.

the equation for the second ship is:

28 * (time) = distance.

since they both travel the same distance when the second ship overtakes the first, then:

25 * (time + .75) = 28 * time

simplify this to get 25 * time + 25 * .75 = 28 * time

simplify further to get 25 * time + 18.75 = 28 * time

subtract 25 * time from both sides of the equation to get 18.75 = 3 * time

solve for time to get time = 18.75 / 3 = 6.25 hours.

in 6.25 hours, the first ship has traveled 25 * (6.25 + .75) = 25 * 7 = 175 kilometers.

in 6.25 hours, the second ship has traveled 28 * 6.25 = 175 kilometers.

they both meet 175 kilometers from their starting point.

the second ship will overtake the first ship in 6.25 hours after the second ship departs.

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