Question

A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip took 2 ​hours?

Answer 1

A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is  9.6 miles

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The speed of an object refers to the change of the object's distance within a specified time.

Mathematically, we can have;

$\mathbf{Speed =\dfrac{distance}{time}}$

Distance = speed × time

From the information given;

• The fisherman row upstream for 4 miles/ hour.
• The distance covered by the fisherman = 4 × t₁  ----- (1)

• The fisherman row downstream at 6 miles/ hour

• The distance covered by the fisherman = 6 × t₂  ------ (2)

• SInce it took the entire trip 2 hours, we can infer that:

• t₁ + t₂ = 2
• t₂ = 2 - t₁

From equation (2), replace the above value of t₂ into equation (2)

• d = 6 t₂
• d = 6(2 - t₁)
• d = 12 - 6t₁

From equation (1)

• d = 4 t₁  

Equation both distance together, we have:

• 12 - 6t₁ = 4t₁
• 12 = 4t₁ + 6t₁
• 12 = 10t₁
• t₁ = 12/10
• t₁ = 1.2  hours

From t₂ = 2 - t₁

• t₂ = 2 - 1.2
• t₂ = 0.8 hours

From d = 4t₁

Replace t₁ with 1.2 hours

• d = 4(1.2 hours)
• d = 4.8 miles

Also, from d = 6t₂

• d = 6(0.8)
• d = 4.8 miles

Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles

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