Question

A boat downstream and covers the distance between two ports in 4 hours. It covers the same distance in 6 hours when it goes upstream. If the speed of the boat is 5km/h. Find the speed of water.

Answer 1

Hint:Assume the total distance between the two ports and the speed of the water. Speed of the downstream is the sum of speed of boat and speed of the water and for the speed of the upstream subtract the speed of the water from the speed of boat.

Complete step by step answer:
We are given the time taken to cover the distance in the upstream and the downstream.
Let the speed of water is $xkm/h$ and the distance between the two ports is $d$
The speed of the boat is $5km/h$.
We know that the speed of the downstream is the sum of speed of boat and speed of the water.
Therefore, speed of the downstream is $5 + x$
For the speed of the upstream, Subtract the speed of the water from the speed of boat.
Therefore, speed of the upstream is $5 - x$
Time is the ratio of total distance travelled and the speed.
Write the mathematical expression for time taken by boat to cover the distance in the upstream and downstream.
For downstream,
$
  \dfrac{d}{{5 + x}} = 4 \\
  d = 4(5 + x)...........(1) \\
 $
For upstream,
$
  \dfrac{d}{{5 - x}} = 6 \\
  d = 6(5 - x)...........(2) \\
 $
Compare both the equations to evaluate the value of $x$.
$
  4(5 + x) = 6(5 - x) \\
  20 + 4x = 30 - 6x \\
  10x = 10 \\
  x = 1 \\
 $

Therefore, the speed of the water is $1km/h$

Note:
When the boat is travelling in the direction of speed of the water then the boat is said to go in the downstream and when the boat is travelling against the speed of the current then the boat is said to go in the upstream.