Every two hours, a ferry leaves Froopaloop Island and heads due east to the mainland, taking exactly one hour. Then it leaves the mainland and heads due west back to the island, again taking exactly one hour. Then it repeats
Instead of taking the ferry to Froopaloop Island, Heather prefers to do something very risky: she dons her
gorgeous white bikini and swims to the island. (The inhabitants of the island don't know what she looks like with
clothes on.)
One day, Heather left the mainland terminal at exactly the same time the
ferry left the island terminal. Exactly
50 minutes later, the ferry passed her.
Assuming both Heather and the ferry travel at a constant speed, and ignoring the time the ferry spends at the mainland terminal, how much time passed between the ferry passing Heather in the opposite direction and passing her in the same
direction?
Hint: Fifty minutes after leaving the island terminal, the ferry will go in the opposite direction of Heather.
Island location = 0
Mainland location = 60 units
Boat speed 60 units/min
Swimmer speed v.
First meet (distance from island) is 50.
Swimmer travelled 10 units in 50 min, v = 0.2 units/min
Swimmer location x = 60 - 0.2*t
Boat positions x = t for 0<t<60
x = 60 - (t-60) for 60<t<120
x = 120 - t for 60<t<120
60 - 0.2*t = 120 - t
.8*t = 60
t = 75; x = 45
The second meet occurs 3/4 of the way from the island to the mainland (45/60). The two meets occurred at 50 and 75 minutes.
The time between meetings was 25 minutes.
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Posted by Larry
on 2024-12-29 19:28:00 |