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26 Apr 2026, 11:07
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A motorboat can travel at a speed of 5 kilometers per hour in still water, and the river current flows at 1 kilometer per hour. The boat travels from a dock to a location upstream and then returns to the dock along the same route, taking a total of 5 hours. How far is the location from the dock?
A. 8 km
B. 10 km
C. 12 km
D. 15 km
E. 18 km
A. 8 km
B. 10 km
C. 12 km
D. 15 km
E. 18 km
26 Apr 2026, 11:07
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Official Solution:
A motorboat can travel at a speed of 5 kilometers per hour in still water, and the river current flows at 1 kilometer per hour. The boat travels from a dock to a location upstream and then returns to the dock along the same route, taking a total of 5 hours. How far is the location from the dock?
A. 8 km
B. 10 km
C. 12 km
D. 15 km
E. 18 km
Upstream speed = \(5 - 1 = 4\) km/h, because the current opposes the boat’s motion and reduces its effective speed relative to the shore.
Downstream speed = \(5 + 1 = 6\) km/h, because the current helps the boat and increases its effective speed relative to the shore.
Let the one way distance from the dock to the location be \(d\) km. Total time is upstream time + downstream time, so:
\(\frac{d}{4} + \frac{d}{6} = 5\)
\(\frac{3d + 2d}{12} = 5\)
\(\frac{5d}{12} = 5\)
\(d = 12\)
Answer: C
A motorboat can travel at a speed of 5 kilometers per hour in still water, and the river current flows at 1 kilometer per hour. The boat travels from a dock to a location upstream and then returns to the dock along the same route, taking a total of 5 hours. How far is the location from the dock?
A. 8 km
B. 10 km
C. 12 km
D. 15 km
E. 18 km
Upstream speed = \(5 - 1 = 4\) km/h, because the current opposes the boat’s motion and reduces its effective speed relative to the shore.
Downstream speed = \(5 + 1 = 6\) km/h, because the current helps the boat and increases its effective speed relative to the shore.
Let the one way distance from the dock to the location be \(d\) km. Total time is upstream time + downstream time, so:
\(\frac{d}{4} + \frac{d}{6} = 5\)
\(\frac{3d + 2d}{12} = 5\)
\(\frac{5d}{12} = 5\)
\(d = 12\)
Answer: C
