Daily Math Puzzle: 2026-07-29
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2026-07-29
In a thrilling race for the legendary 'Sunken Pearl', two rival captains, Blackheart and Pete, set sail for a remote island 100 nautical miles away. Each captain employs a different strategy: * **Captain Blackheart** sails the first *half of the total distance* at a blistering 10 knots. For the remaining *half of the total distance*, he conserves fuel and sails at a slower 5 knots. * **Smuggler Pete**, planning his journey differently, sails for the first *half of his total travel time* at a rapid 10 knots. For the second *half of his total travel time*, he drops to a more relaxed 5 knots. Assuming they start simultaneously and face no other obstacles, who reaches the treasure island first?
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Solution
Smuggler Pete — Let the total distance to the island be D = 100 nautical miles.
**Captain Blackheart's Journey:**
Captain Blackheart sails half the distance (D/2 = 50 miles) at 10 knots and the other half (50 miles) at 5 knots.
Time for the first half of distance (T1) = Distance / Speed = 50 miles / 10 knots = 5 hours.
Time for the second half of distance (T2) = Distance / Speed = 50 miles / 5 knots = 10 hours.
Total time for Captain Blackheart = T1 + T2 = 5 hours + 10 hours = 15 hours.
**Smuggler Pete's Journey:**
Let T_Pete be Smuggler Pete's total travel time. He sails for half of his total travel time (T_Pete/2) at 10 knots and for the other half of his total travel time (T_Pete/2) at 5 knots.
Distance covered in the first half of time (D1) = Speed × Time = 10 knots × (T_Pete/2) = 5 * T_Pete miles.
Distance covered in the second half of time (D2) = Speed × Time = 5 knots × (T_Pete/2) = 2.5 * T_Pete miles.
The total distance covered by Smuggler Pete is D1 + D2 = 5 * T_Pete + 2.5 * T_Pete = 7.5 * T_Pete.
We know the total distance to the island is 100 nautical miles, so:
7.5 * T_Pete = 100
T_Pete = 100 / 7.5 = 100 / (15/2) = 200 / 15 = 40/3 hours.
40/3 hours is approximately 13.33 hours, or 13 hours and 20 minutes.
**Conclusion:**
Captain Blackheart takes 15 hours to reach the island.
Smuggler Pete takes 13 hours and 20 minutes to reach the island.
Therefore, Smuggler Pete reaches the treasure island first.
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