A boat travels 30 km upstream and in the same time it travels 50 km downstream. The speed of the stream is 5 km/hr. What is the speed of the boat in still water? What is the distance between the 2 ports?
2007-08-17 20:11:41 · 4 answers · asked by Titanic lover 2 in Science & Mathematics ➔ Mathematics
Let v be the speed of the boat in still water.
30/(v-5) = 50/(v+5)
3v+15 = 5v-25
v = 20 km/hr
d = 50 - 30 = 20 km downstream
2007-08-17 20:26:08 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋
Let the speed of the boat be x km/hr in still water.
Therefore according to the problem,
30/(x-5)=50/(x+5)
or3/(x-5)=5/(x+5) [dividing both sides by 10]
or5x-25=3x+15 [by cross multiplication]
or,5x-3x=15+25
or,2x=40
or,x=40/2=20
Therefore the speed of the boat in still water is 20 kmph .
2007-08-18 03:39:27 · answer #2 · answered by alpha 7 · 1⤊ 0⤋
Let speed in still water = x mph
********Downstream***Upstream
D (km)******50 *************30
S (km/h)*****(x + 5) ********(x - 5)
T (h)********50 / (x + 5) ***30 / (x - 5)
50 / (x + 5) = 30 / (x - 5)
50x - 250 = 30x + 150
20x = 400
x = 20
Speed in still water = 20 mph
Distance between ports = (50 + 30) km = 80 km
2007-08-18 06:34:22 · answer #3 · answered by Como 7 · 0⤊ 0⤋
let the speed of the boat be x km\hr
then speed upstream=x-5km\hr
speed downstream=x+5km\hr
speed=distance\time,thus time=distance\speed
so we have the equation
30\x-5=50\x+5
=30x+150=50x-250
=x=20
2007-08-18 03:34:36 · answer #4 · answered by ishika 1 · 0⤊ 0⤋