Question

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Answer 1

Hello bro....

Answer:

Rowing Speed = 8 km/hr

Stream Speed = 4 km/Hr

Step-by-step explanation:

A person can row a boat 8km upstream and 24km downstream in 4hours he can row 12km downstream and 12km upstream in 4hours find the speed of rowingvand speed of the current

Let Say speed of Rowing = R km/Hr

Speed of Stream = S km/Hr

Up Stream Speed = R - S Km/Hr

Down Stream Speed = R + S Km/Hr

Distance = Speed * Time

Time = Distance / Speed

8km upstream and 24km downstream in 4hours

8/(R-S) + 24/(R+S) = 4

Dividing both sides by 4

=> 2/(R-S) + 6/(R+S) = 1

Multiplying both sides by (R+S)(R-S)

=> 2R + 2S + 6R - 6S = R² - S²

=> 8R - 4S = R² - S²  - Eq 1

12km downstream and 12km upstream in 4hours

12/(R-S) + 12/(R+S) = 4

Dividing both sides by 4

=> 3/(R-S)  + 3/(R+S) = 1

=> 3R + 3S + 3R - 3S = R² - S²

=> 6R = R² - S²  - Eq 2

Equating Eq 1 & Eq2

8R - 4S = 6R

=> 2R = 4S

=> R = 2S

Putting in Eq 2

6 × 2S = (2S)² - S²

=> 12S = 4S² - S²

=> 12S = 3S²

Dividing by 3S both sides

=> 4 = S

Hence speed of stream = 4 km/Hr

Speed of rowing = 2S = 2×4 = 8 km/Hr

Hope helps........