Question

It took Jack 2 hours to paddle 6.4 km upstream on the Black River to the giant's castle. The speed of the river is 1.8 km/h. How long will it take Jack to cross Swan Lake if the lake is 2.5 km long?

Answer 1

To find the time Jack takes to cross Swan Lake, his average speed is required:

The time it will take Jack to cross Swam Lake is 0.5 hours

Reason:

Time it took Jack to paddle 6.4 km upstream, t = 2 hours

Distance Jack paddled, d = 6.4 km

The given speed of the Black River, v₂ = 1.8 km/h

The width of the lake, w = 2.5 km

The time it will take Jack to cross Swan Lake

Let v₁, represents Jack's speed, we have;

$v_1 - v_2 = \dfrac{d}{t}$

Therefore;

$v_1 - 1.8 = \dfrac{6.4}{2} = 3.2$

v₁ = 3.2 + 1.8 = 5

• Jack's speed, v₁ = 5 km/h

$Time \ to \ cross \ the \ lake , \ t_S = \dfrac{w}{v_1}$

$t_S = \dfrac{2.5 \, km}{5 \, km/h} = 0.5 \, hr.$

The time it will take Jack to cross Swan Lake, $t_S$ = 0.5 hours

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