Given:
rate in still water = 8 kph ( I just assumed that it is what the question meant)
time taken to travel a given distance upstream = 5 hours
time taken to travel the same distance downstream = 3 hours
Hidden Clue:
The distances taken to travel downstream and upstream are the same.
Find:
Rate of the current
Solution:
What we need to find is the rate of the current. Let the rate of the current be x.
(Let us settle with the units later.)
When the boat travels upstream:
Speed = Rate in still water - rate of current (It is like that because when traveling upstream, the speed of the boat is decreased because of the current)
= 8 - x
Time = 5
Disance = ST
= 5 ( 8-x )
When the boat travels downstream:
Speed = Rate in still water + rate of current
8 + x
Time = 3
Distance = ST
= 3 (8+x)
Since, their distances are the same, then it becomes like this:
5 (8-x) = 3 (8+x)
40 - 5x = 24 + 3x
40 = 24 + 3x + 5x
40 = 24 + 8x
40 - 24 = 8x
16 = 8x
[tex] \frac{16}{8} [/tex] = [tex] \frac{8x}{8} [/tex]
2 = x
Check:
5 ( 8 - 2) = 3 (8 + 2)
5 ( 6) = 3 ( 10 )
30 = 30, CORRECT
Final Answer:
The rate of the current is 2 kph.
