A man goes to place of distance 8 km and returns to the same place by boat in 4 hours 16 minutes. If the speed of the stream is 1km/hr., find the speed of the boat in still water.
Answers
Answer:
Answer:
4 km/hr
Step-by-step explanation:
Let v be the speed of the boat in still water in km/hr. So v > 0.
The speed downstream is then v+1 and the speed upstream is v-1, allowing for the effect of the moving water.
The time taken to travel the 8 km downstream is then:
time = distance / speed = 8 / (v + 1)
The time taken to travel the 8 km upstream is similarlay: 8 / (v - 1)
The total time is:
4 hrs 16 min = ( 240 + 16 ) / 60 hrs = 256 / 60 hrs = 64 / 15 hrs. Hence...
64/15 = 8/(v + 1) + 8/(v - 1)
=> 8/15 = 1/(v + 1) + 1/(v - 1) [ divided both sides by 8 ]
=> 8 ( v² - 1 ) = 15 ( v - 1 ) + 15 ( v + 1 ) [ multiplied by 15(v-1)(v+1) ]
=> 8v² - 8 = 30v
=> 4v² - 15v - 4 = 0
=> v = ( 15 ± √(15² - 4(4)(-4)) ) / (2×4)
= ( 15 ± √(225 + 64) ) / 8
= ( 15 ± √289 ) / 8
= ( 15 ± 17 ) / 8
= ( 15 + 17 ) / 8 [ since v > 0 ]
= 32 / 8
= 4
So the speed of the boat on still water is 4 km/hr.