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A man rows a boat and takes 120 minutes when he goes 17 km upstream and 27 km downstream. In another round, he goes 51 km upstream and 36 km downstream in total time of 270 minutes. What is the speed of the boat in still water and the speed of stream?

A man rows a boat and takes 120 minutes when he goes 17 km upstream and 27 km downstream. In another round, he goes 51 km upstream and 36 km downstream in total time of 270 minutes. What is the speed of the boat in still water and the speed of stream? Correct Answer 250/11 km/hr, 80/11 km/hr

Given:

During first visit,

Upstream distance = 17 km

Downstream distance = 27 km

During second visit,

Upstream distance = 51 km

Downstream distance = 36 km

Total time taken during first visit = 120 mins.

Total time taken during second visit = 270 mins.

Concept Used:

Time = Distance/Speed

Formula Used:

D = B + S

U = B – S

B = (D + U)/2

S = (D – U)/2

where, D → Downstream speed, U → Upstream speed, B → Speed of boat in still water, S → Speed of stream.

Calculations:

Time taken during first visit = 120 mins. = 120/60 hrs.

⇒ Time taken during first visit = 2 hrs.

Time taken during second visit = 270 mins. = 270/60 hrs.

⇒ Time taken during second visit = 9/2 hrs.

Time = Distance/Speed

During first visit,

17/U + 27/D = 2      ----(1)

During second visit,

51/U + 36/D = 9/2      ----(2)

Multiplying (1) by 3 and subtracting (2) from (1), we get

51/U + 81/D = 6     

51/U + 36/D = 9/2

⇒ (81/D – 36/D) = (6 – 9/2)

⇒ 45/D = 3/2

⇒ D = 30 km/hr

Putting D in (2)

⇒ 51/U + 36/30 = 9/2

⇒ 51/U = 33/10

⇒ U = 170/11 km/hr

B = (D + U)/2

⇒ B = (30 + 170/11)/2

⇒ B = 250/11 km/hr

S = (D – U)/2

⇒ S = (30 – 170/11)/2

⇒ S = 80/11 km/hr

∴ The speed of the boat in still water and speed of stream is 250/11 km/hr and 80/11 km/hr respectively.

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