a boat covers 32 km upstream and 36 km downstream in 7 hours.also it covers 40 km upstream and 48 km downstream in 9 hours.find the speed of the boat on still water and that of stream.
Answers
40/x-Y+48/x+y=9 ----------(2)
after solving we get x=10,y=2
speed of boat is 10 km/hr
speed of stream 2 km/hr
I find that in this question the first doubt of students is about what is upstream and downstream.
Upstream : When you flow against waves
Downstream : When you flow along with waves.
Let the speed of boat be x km/h and of streams be y km/h. Then naturally, final speed in :
Upstream = x - y (Since boat have to flow against)
Downstream = x + y (Since boat will flow along)
Equation (1) : 32/(x - y) + 36/(x + y) = 7
Take 1/(x - y) = u and 1/(x + y) = v
⇒ 32u + 36v = 7
Equation (2) : 40/(x - y) + 48/(x + y) = 9
⇒ 40u + 48v = 9
By doing 5 × (1) and 4 × (2) we get,
⇒ 160u + 180v = 35 __(3)
⇒ 160u + 192v = 36 __(4)
Doing (4) - (3)
⇒ 12v = 1 or v = 1/12
Therefore, 40u + 48(1/12) = 9
⇒ u = 5/40 or 1/8
Since 1/(x - y) = u and 1/(x + y) = v,
→ x - y = 8 and x + y = 12
On adding both we get,
→ 2x = 20 or x = 10
Hence, y = 12 - 10 = 2
Hence speed of boat in still water is 10 km/h and of stream is 2 km/h.