SOLUTION: A riverboat travels 87 km downstream in 3 hours. It travels 76 km upstream in 4 hours. Find the speed of the boat and the speed of the water.
Question 1059753: A riverboat travels 87 km downstream in 3 hours. It travels 76 km upstream in 4 hours. Find the speed of the boat and the speed of the water. Found 2 solutions by jorel555, addingup:Answer by jorel555(1290) (Show Source):
You can put this solution on YOUR website! Let s be the speed of the boat, and c be the speed of the current. Then:
87/(s+c)=3
3s+3c=87, and
76/(s-c)=4
4s-4c=76. So:
12s+12c=348
12s-12c=228
24s=576
s=24
c=5
The boat goes 24 kph; the current is 5 kph. ☺☺☺☺
You can put this solution on YOUR website! Let x = speed of boat in still water
Let y = speed of the current
then
(x+y) = speed with the current
and
(x-y) = speed against the current
:
Write a distance equation for each trip:
Distance = time * speed
3(x + y) = 87
4(x - y) = 76
:
x + y = 29
x - y = 19
Add these two equations and you get:
x+x = 2x
y+-y = 0
29+19 = 48
Write your new equation:
2x = 48
x = 24 mph is the speed in still water
:
The speed of the current:
We said x+y = 29, 24+y = 29, y = 5 this is the speed of the water
Or you can do it with x-y=19; y = x-19, y = 24-19 = 5 again, 5 is the speed of the water whether going up river or down river (of course, downriver it pushes you faster and upriver it slows you down)
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