SOLUTION: Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island off the coast of Massachusetts. Two hours later, a to

Question 1166177: Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island off the coast of Massachusetts. Two hours later, a tour boat leaves the same dock and travels at an average speed of 27 mph toward the same island. How many hours after the tour boat leaves will Michael's boat be alongside the tour boat?
Found 3 solutions by Theo, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
r * t = d
r = rate of speed
t = time
d = distance

9 * t = d = rate * time for the motor boat.
27 * (t - 2) = d = rate * time for the tour boat.

they will meet up with each other when they both travel the same distance in the same time.

since they both travel the same distance of d, then:
9 * t = 27 * (t - 2)
simplify to get:
9 * t = 27 * t - 54
subtract 9 * t from both sides of the equation and add 54 to both sides of the equation to get:
18 * t = 54
solve for t to get:
t = 3

the motor boat will have traveled at 9 mph for 3 hours to make a distance of 9 * 3 = 27 miles.
the tour boat will have traveled at 27 mph for 1 hour to make a distance of 1 * 27 = 27 miles.

since the tour boat left the dock 2 hours after the motor boat, they will both meet up with each other 27 miles from the same dock that they both departed after 3 hours have elapsed.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island off the coast of Massachusetts. Two hours later, a tour boat leaves the same dock and travels at an average speed of 27 mph toward the same island. How many hours after the tour boat leaves will Michael's boat be alongside the tour boat?

Let time it takes the tour bus to get to "catch-up" point, be T
Then time it takes the motorboat to get to the "catch-up" point = T + 2
As distances are the same, we get: 9(T + 2) = 27T
9T + 18 = 27T
18 = 27T - 9T
18 = 18T
Time it takes the tour bus to get to "catch-up" point, or
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

When the tour boat leaves, Michael has been traveling for 2 hours at 9 mph, so he has gone 18 miles.

The rate at which the tour boat overtakes the motorboat is (27-9) = 18 mph.

The number of hours the tour boat takes to make up 18 miles at the rate of 18 mph is 18/18 = 1.

ANSWER: 1 hour

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