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

Let the distance travelled by the man in upstream be x. Given that,

• Speed while upstream = 3 km/h
• Speed while downstream = 5 km/h
• Time taken = 48 minutes

Here, It is clear that the man will cover same distance while going upwards and downwards as well.

We know,

⇒ Time = Distance / Speed

So,

⇒ Time taken in Upstream + Time taken in downstream = 48 minutes

Since, The speed is given in hour, So, we must convert time into hour as well.

⇒ x/3 + x/5 = 0.8

⇒ (5x + 3x)/15 = 0.8

⇒ 8x / 15 = 0.8

⇒ 8x = 12

⇒ x = 3/2

⇒ x = 1.5 km

Hence, Man went 1.5 km upstream.

Answer 2

$\bf \huge \pink ◆ Answer -$

Distance travelled upstream = 1.5 km

$\bf \huge \pink ◆ Explanation -$

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)

$\bf \{\pink s = 1.5 km \}$

Therefore, the man went 1.5 km upstream.