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satela [25.4K]
3 years ago
13

Hi guys . pls help me with this​

Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Step-by-step explanation:

The upstream speed is S / t₁, and the downstream speed is S / t₂.

If we say f is the speed of the fish in calm water, and r is the speed of the river, then:

f − r = S / t₁

f + r = S / t₂

If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.

Using Pythagorean theorem:

f² = (ℓ/T)² + r²

f² − r² = (ℓ/T)²

(f − r) (f + r) = (ℓ/T)²

(S / t₁) (S / t₂) = (ℓ/T)²

S² / (t₁ t₂) = (ℓ/T)²

(t₁ t₂) / S² = (T/ℓ)²

√(t₁ t₂) / S = T/ℓ

T = ℓ√(t₁ t₂) / S

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