##### Maths Tricks

# Maths Tips Boat and Stream, Formulas, Problems

Here we are listed All the Important terms, Formulas, Problems of Boat and Stream on General Aptitude. Those Maths Tips will help you get maximum marks from this section. This file will be updated regularly, So please bookmark this page on your browser to get latest updates. You can also download the PDF file of the following below.

Important Terms

u – Speed of boat/man |

v – Speed of water |

Formulas

Speed of boat along the river (Downstream) a = u + v |

Speed of boat against the river (Upstream) b = u – v |

Mostly speed if boat greater than speed of water |

Speed of boat in still water u = ½(a + b) |

Speed of water current v = ½(a – b) |

Distance = time (u^{2 }– v^{2})/ 2u |

#### Problem:

**1)** A man can row 18km/hr in still water. speed of the man in downstream is thrice the speed in upstream. Find the rate of stream.

**Solution:**

*Let, Speed of man in upstream a = a*

Speed* of man in downstream b = 3a*

Speed* of man in still water u = ½(a + b)*

*Speed of man in still water = ½(3a + a) = 2a*

*We know *speed* of man in still water = 18*

*So, a = 9*

*Rate of stream = ½(27 – 9) =9 km/hr*

**2)** A boat can cover certain distance in downstream in 1hr. and it takes 1½hr to cover same distance in upstream. If speed of the stream is 3kmph, then what will be the speed of boat?

**Solution:**

*let *speed* of *boat* in still water be x*

*speed in downstream = x + 3*

*speed in upstream = x – 3*

*Since boat covered *same* distance in upstream and downstream,*

*(x + 3)*1 = (x – 3)*(3/2)*

*speed in downstream x= 15 *kmph

*3) A man can row *three quarter* of a km against the stream in 11¼ min and down the stream in 7½min. what is the speed of man in still *water.

**Solution:**

*Speed of man in Upstream = ((¾)/(45/4)) *60*

*= 4 *kmph

*Speed of man in Downstream = ((¾)/(15/4))* 60*

*= 12 *kmph

Speed* of man in still water u = ½(a + b)*

*Speed of man in still water = (12 + 4)*½ = 8 *kmph

**4)** A streamer takes 3hr to cover a distance of 24km upstream, if the rate of stream is 3 kmph. Then find the speed of streamer in still water.

**Solution**:

*Upstream speed = 24/3 =8kmph*

*Rate of stream = 3kmph*

Speed* of streamer – *rate* of stream = upstream*

*Speed of streamer = 11kmph*

**5)** The distance between two points is 36km. A boat rows in still water at 6kmph, it takes 8hr less to cover dist in downstream in comparison to that in upstream. Find the rate of stream.

**Solution**:

*Time = distance * speed*

*Difference between time taken to cover upstream and downstream is 8hr*

*(36/(6-x)) – (36/(6+x)) = 8*

*36(6+x) – 36(6-x) = 8(36-x ^{2})*

*9x = 36- x ^{2}*

*x ^{2}+9x-36 = 0 (to find value of x use quadratic equation technique)*

*(x+12)(x-3)=0*

*Speed cannot be negative so x = 3kmph*

*Rate of stream = 3kmph*

Sample problems are here, more problems will be added soon.