Steve motored a boat upstream, and a 45-mile trip took him five hours. The next day, his return trip downstream took 3 hours. Find the speed of the current.
2007-06-17 18:25:03 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
45/5 = 9mph
45/3 = 15 mph
Find the average speed and then you will see how fast the current effected him.
Avg. = 12mph
Current was 3mph. It was against him on the way there, with him on the way back.
2007-06-17 18:35:41 · answer #1 · answered by Anonymous · 0⤊ 0⤋
let x be the speed of current & y of boat.
Effective speed upstream =distance/time=45/5
=9 miles per hour
Effective speed downstream = 45/3
=15 miles per hour
Therefore,
y-x=9
y+x=15
Add both the equations
2y=24
y=12
Put this value in first equation
12-x=9
x=3
Speed of current is 3 miles/hr.
2007-06-18 01:38:12 · answer #2 · answered by Jain 4 · 1⤊ 0⤋
OK, if the speed of the boat is x, and the current is C, since distance =rate x time we know that his upward speed has to have been 9 mph and his downward speed 15.
so:
9=x-c
15=x+c
and so 24 = 2x; x=12 was his boat speed, and 3 mph the current.
2007-06-18 01:33:35 · answer #3 · answered by Mark S, JPAA 7 · 1⤊ 0⤋
First trip 9 miles per hour
Second Trip 15 miles per hour.
The difference in the two is 6 miles per hour.
Divide that in half and you get 3 mph is the stream speed.
You went both ways. The boat was travelling at 12mph without current
2007-06-18 01:31:39 · answer #4 · answered by lovingdaddyof2 4 · 1⤊ 0⤋
Let b = speed of boat and c = speed of current.
(rate)(time) = distance
Upstream; current reduces the boat's speed relative to land
(b - c)5 = 45
b - c = 9
Downstream; current increases the boat's speed relative to land
(b + c)3 = 45
b + c = 15
We have a system of linear equations that we can solve by the addition method.
b - c = 9
b + c = 15
adding
2b = 24
b = 12 and c = 3
Answer: The speed of the current is 3 miles per hour.
2007-06-18 01:39:09 · answer #5 · answered by mathjoe 3 · 1⤊ 0⤋
Let speed of stream = s mph
speed of boat = b mph
distance d = 45 mile
while going upstream, speed = b-s
45/(b-s)=5
b-s=9 .........................(i)
While going downstream, speed = b+s
45/(b+s)=3
b+s=15 ........................(ii)
Adding (i) & (ii)
2b=24
b=12
Putting b=12 in (i), we get
12 - s = 9
s=3
Thus, Speed of boat=12 mph
and speed of stream=3 mph
2007-06-18 02:43:13 · answer #6 · answered by CrazyCoder 3 · 0⤊ 0⤋
Vb - Vs = 9
Vb + Vs = 15
-Vb + Vs = -9
2Vs = 6
Vs = 3 mph
2007-06-18 01:35:01 · answer #7 · answered by Helmut 7 · 1⤊ 0⤋