A person takes 4 hours 30 minutes to row a boat 16 km downstream of a river and 2 hours 15 minutes to cover a distance of 4 km upstream. find the speed of the river current.
Answers
Let the speed of the boat be x
And the speed of the stream be y
Downstream:
Speed = ( x + y) km/h
Distance = 16 km
Time = 4 hours 30 mins = 4.5 hours
Distance = Speed x Time
16 = 4.5( x + y)
Upstream:
Speed = ( x - y) km/h
Distance = 4 km
Time = 2 hours 15 min = 2.25 hours
Distance = Speed x Time
4 = 2.25 (x - y)
Putting the two equations together:
16 = 4.5( x + y) ----------------------- [ 1 ]
4 = 2.25 (x - y) ----------------------- [ 2 ]
From [ 1 ]:
16 = 4.5( x + y)
16 = 4.5x + 4.5y ----------------------- [ 3 ]
From [ 2 ] :
4 = 2.25 (x - y)
4 = 2.25 x - 2.25 y
8 = 4.5x - 4.5y ----------------------- [ 4 ]
[ 3 ] + [ 4 ]:
24 = 9x
x = 8/3 km/h ----------- sub into [ 3 ] to find y
Find y :
16 = 4.5x + 4.5y
16 = 4.5 (8/3) + 4.5y
16 = 12 + 4.5y
4.5y = 4
y = 8/9 km/h
Answer: The speed of the stream is 8/9 km/h
Let assume speed of boat to be x, and speed of stream to be y,
Distance = 16 km, time = 4 hours 30 minutes (4.5 hours) For downstream,
Speed = x+y, Distance = speed x time,
16= 4.5(x+y), evaluate upstream,
Speed = x-y, distance = 4 km,
time = 2 hours 15 minutes (2.25 hours),
Calculate distance, 4= 2.25 (x-y),
consider 16= 4.5(x+y)-----1, 4= 2.25 (x-y)--------
2, evaluate equation 1, 16=4.5x +4.5y-----3,
from equation 2 you get equation as 4=2.25 X+2.25y-------4,
then add equation 3 and 4, you get 24= 9x, x = 8/3 km/ hr.
To find you subtract x value into equation 3 and you acquire y value as 8/9 km/hr.