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Question

The Queen Mary can make a 12-mile trip down the port of Long Beach and back in a total of 1.5 hours. If the boat travels 15mph in still water, find the speed of the current of the port of Long Beach

Answer 1

Total Distance travelled by Queen Mary is 12 mile

Distance covered by Mary while travelling towards the Long Beach is d₁ = 6 miles.

Distance covered by Mary while returning back is d₂ = 6 miles.

Speed of the Boat is b = 15 mph

Total time taken is 1.5 hours

We know that Speed  = Distance/time

time = Distance / Speed

Let us consider the speed of the current is x.

Speed of the motor boat along the current y₁ = 15 + x

Speed of the motor boat against the current y₂ = 15 - x

Time taken by motor boat while going is t₁ = d₁ / y₁ = 6/(15+x)

Time taken by motor boat while returning back is t₂ = d₂ / y₂ = 6/(15-x)

Total time = t₁ + t₂

Total time = 6/(15+x) + 6/(15-x)

x² = 225 - 120

x² = 105

x = 10.24 mph

Therefore Speed of the current is 10.24 mph.

Comments

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Yes, the provided answer is correct.