Question: Rahman is a boatman. He can row a boat at the speed of 5 km/hr upstream and 15 km/hr downstream. Find the speed of the stream.

Solution:

Let’s denote:

B as Speed of the boat in still water (km/h)

S as Speed of the stream (km/h)

Speed of the boat upstream is the speed of the boat in still water minus the speed of the stream:

B - S = 5 km/hr -------- (1)

Speed of the boat downstream is the speed of the boat in still water plus the speed of the stream:

B + S = 15 km/hr -------- (2)

(1) + (2)

B - S = 5

B + S = 15

2B = 20

∴ B = 10 km/hr

Putting the value of B in (2)

∴ S = (15 - 10) km/hr = 5 km/hr

∴ The speed of the stream is 5 km/hr

হ্যাঁ, পুরো সমাধান ঠিক হয়েছে ✅

রাউন্ড-ট্রিপে গড় গতি = হারমোনিক গড়

$$v_{\text{avg}}=\frac{2ab}{a+b}=\frac{2\times 6\times 3}{6+3}=\frac{36}{9}=4 \text{ কি.মি./ঘণ্টা}$$

দ্রুত যাচাই (ধরি দূরত্ব $ক=6$ কি.মি.):

• যাওয়া: $6/6=1$ ঘণ্টা

• ফেরা: $6/3=2$ ঘণ্টা

• মোট দূরত্ব: $12$ কি.মি., মোট সময়: $3$ ঘণ্টা ⇒ $12/3=4$ কি.মি./ঘণ্টা ✔️

উত্তর: ৪ কি.মি./ঘণ্টা

Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

Solution:

Relative speed of the thief and policeman  =  (11 - 10) km/hr = 1 km/hr 

Distance covered in 6 minutes  = (1/60) × 6 km   = 1/10 km = 100 m

Therefore, Distance between the thief and policeman = (200 - 100) m = 100 m.