Subjects algebra

Boat Speed

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1. **Problem:** A boat travels at 15 km/hr in still water and the stream speed is 5 km/hr. Find the time to travel 60 km downstream. 2. **Formula:** Downstream speed = speed of boat + speed of stream. 3. **Calculation:** Downstream speed = 15 + 5 = 20 km/hr. 4. **Time taken:** Time = Distance / Speed = 60 / 20 = 3 hours. 5. **Answer:** (a) 3 hours. 1. **Problem:** Boat speed 12 km/hr, stream speed 4 km/hr, find time for 48 km downstream. 2. **Downstream speed:** 12 + 4 = 16 km/hr. 3. **Time:** 48 / 16 = 3 hours. 4. **Answer:** (a) 3 hours. 1. **Problem:** Boat speed 25 km/hr, stream speed 5 km/hr, round trip time 5 hours, find one-way distance. 2. **Speeds:** Downstream = 25 + 5 = 30 km/hr, Upstream = 25 - 5 = 20 km/hr. 3. **Let distance = d km.** Total time = d/30 + d/20 = 5. 4. **Solve:** Multiply both sides by 60: 2d + 3d = 300 => 5d = 300 => d = 60 km. 5. **Answer:** (c) 60 km. 1. **Problem:** Boat takes 5 hours upstream and 2 hours downstream for 40 km each way. Find boat speed in still water. 2. **Speeds:** Upstream speed = 40/5 = 8 km/hr, Downstream speed = 40/2 = 20 km/hr. 3. **Boat speed:** (Upstream speed + Downstream speed)/2 = (8 + 20)/2 = 14 km/hr. 4. **Answer:** (c) 14 km/hr. 1. **Problem:** Boat covers 80 km downstream in 4 hours and upstream in 5 hours. Find boat speed in still water. 2. **Speeds:** Downstream speed = 80/4 = 20 km/hr, Upstream speed = 80/5 = 16 km/hr. 3. **Boat speed:** (20 + 16)/2 = 18 km/hr. 4. **Answer:** (b) 18 km/hr. 1. **Problem:** Man rows at 8 km/hr in still water, stream speed 2 km/hr, find time to row 40 km downstream. 2. **Downstream speed:** 8 + 2 = 10 km/hr. 3. **Time:** 40 / 10 = 4 hours. 4. **Answer:** (b) 4 hours. 1. **Problem:** Boat travels 120 km downstream in 3 hours and upstream in 6 hours. Find stream speed. 2. **Speeds:** Downstream speed = 120/3 = 40 km/hr, Upstream speed = 120/6 = 20 km/hr. 3. **Stream speed:** (Downstream speed - Upstream speed)/2 = (40 - 20)/2 = 10 km/hr. 4. **Answer:** (a) 10 km/hr. 1. **Problem:** Boat travels 180 km downstream in 6 hours and upstream in 9 hours. Find boat speed in still water. 2. **Speeds:** Downstream speed = 180/6 = 30 km/hr, Upstream speed = 180/9 = 20 km/hr. 3. **Boat speed:** (30 + 20)/2 = 25 km/hr. 4. **Answer:** (b) 25 km/hr.