Question

A man rows upstream in still water at 3 km/h and back to the same place at 5 km/h; he takes 48 minutes altogether. How far upstream did he go?​

Answer 1

Given :-

• A man rows upstream in still water at 3 km/h and back to the same place at 5 km/h; he takes 48 minutes altogether.

To Find :-

• How far upstream did he go

Answer :-

Let the distance of upstream x km.

As we know that,

• Time = Distance ÷ Speed

Therefore,

• Time taken to go upstream = x ÷ 3 hours.
• Time taken to go downstream = x ÷ 5 hours.
• Total time = 48 minutes = 48 ÷ 60 hrs = 4 ÷ 5 hrs

According to Question :

→ (x/3) + (x/5) = 4/5

→ 5x + 3x/15 = 4/5

→ 8x/15 = 4/5

→ (8x)(5) = (4)(15)

→ 40x = 60

→ x = 60 ÷ 40

→ x = 6 ÷ 4

→ x = 1.5 km/hr

Therefore,the man went 1.5 km upstream.

Answer 2

Answer:

Distance travelled upstream = 1.5 km

◆ Explanation -

Let s be the distance man go to. Also vm amd vr be velocity of man and that of riverstream respectively.

During upstream journey,

t1 = s / (vm-vr)

t1 = s / 3

During downstream journey,

t2 = s / (vm+vr)

t2 = s / 5

Total time taken is 48 min,

t = t1 + t2

0.8 = s/3 + s/5

0.8 = s × (3+5)/(5×3)

s = 1.5 km

Therefore, the man went 1.5 km upstream.