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16 Sep 2014, 00:46
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A speedboat, when traveling at a speed of 35 km/h, reaches the port 2 hours behind schedule. However, if its speed is increased to 50 km/h, it arrives 1 hour ahead of schedule. At what speed should the boat travel to reach the port exactly on time?
A. 42.00 kmh
B. 43.50 kmh
C. 43.75 kmh
D. 44.25 kmh
E. 44.50 kmh
A. 42.00 kmh
B. 43.50 kmh
C. 43.75 kmh
D. 44.25 kmh
E. 44.50 kmh
16 Sep 2014, 00:46
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Official Solution:
A speedboat, when traveling at a speed of 35 km/h, reaches the port 2 hours behind schedule. However, if its speed is increased to 50 km/h, it arrives 1 hour ahead of schedule. At what speed should the boat travel to reach the port exactly on time?
A. 42.00 kmh
B. 43.50 kmh
C. 43.75 kmh
D. 44.25 kmh
E. 44.50 kmh
Let's use \(t\) as the scheduled time for the boat to reach the port.
At 35 km/h, taking \(t + 2\) hours, the distance is \(D = 35(t + 2)\).
At 50 km/h, taking \(t - 1\) hours, the distance is \(D = 50(t - 1)\).
Equating these distances:
\(35(t + 2) = 50(t - 1)\)
From this, we get \(t = 8\)
Using the 50 km/h speed for reference:
\(D = 50(t - 1)=50*7 = 350\) km.
To determine the required speed:
Speed = \(\frac{350}{8} = 43.75\) km/h.
The boat should travel at 43.75 km/h to arrive on time.
Answer: C
A speedboat, when traveling at a speed of 35 km/h, reaches the port 2 hours behind schedule. However, if its speed is increased to 50 km/h, it arrives 1 hour ahead of schedule. At what speed should the boat travel to reach the port exactly on time?
A. 42.00 kmh
B. 43.50 kmh
C. 43.75 kmh
D. 44.25 kmh
E. 44.50 kmh
Let's use \(t\) as the scheduled time for the boat to reach the port.
At 35 km/h, taking \(t + 2\) hours, the distance is \(D = 35(t + 2)\).
At 50 km/h, taking \(t - 1\) hours, the distance is \(D = 50(t - 1)\).
Equating these distances:
\(35(t + 2) = 50(t - 1)\)
From this, we get \(t = 8\)
Using the 50 km/h speed for reference:
\(D = 50(t - 1)=50*7 = 350\) km.
To determine the required speed:
Speed = \(\frac{350}{8} = 43.75\) km/h.
The boat should travel at 43.75 km/h to arrive on time.
Answer: C
25 Aug 2023, 01:12
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
