Posted by Jessica on Thursday, November 16, 2006 at 5:30pm.
A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.
The speed is 6 mph slower going upstream and 6 mph faster going downstream. Distance traveled = time x speed. The distance for both is equal. Let X = the speed in still water.
With the above information, you should be able to develop the equation and solve it for X.
I hope this helps. Thanks for asking.
Let y = speed of the kayaker.
distance = rate x time.
For the trip down stream, his rate is y+6 and his rate back up stream is y-6.
The distance traveled is the same; therefore,
upstream rate x time = downstream rate x time
Solve for y.
Post your work if you get stuck.
You just give names to the variables you don't know and write down the equations.
The speed the kayaker in still water? Don't know? Let's call it v.
Then the speed when travelling with the current is
v + 6 mph.
The distance traveled in the two hours is:
(v + 6 mph)* 2 hours
let's call this d, so we put:
d = (v + 6 mph)* 2 hours
The speed on the return trip is
v - 6 mph
The time mneeded for that is given to be 3 hours, but it is also equal to the distance divided by the speed. So, you have that:
d/(v-6 mph) = 3 hours -->
(v + 6 mph)* 2 hours/(v-6 mph) = 3 hours --->
(x+6)/(x-6) = 3/2
where x = v/(mph)
x + 6 = 3/2 x - 9 --->
1/2 x = 15 --->
x = 30 -->
v/(mph) = 30 --->
v = 30 mph
Answer This Question
More Related Questions
- Math - A kayaker paddled 2 hours with a 6 mph current in a river. The return ...
- Algebra - Cody’s motorboat took 3 hr to make a trip downstream with a 6-mph ...
- math - donna took 3hours to row 18 km upstream. her return trip took 1 hour less...
- math - The Connecticut River flows at a rate of 5 km / hour for the length of a ...
- Algebra - on a canoe trip, Rita paddled upstream (against the current) at an ...
- algebra - Chen's motorgoat took 3 hr to make a treip downstream with a 6-mph ...
- Math - 1.A tour boat on a river traveled 40 miles downstream in 4 hours. The ...
- Algebra - The Connecticut River flows at a rate of 3 km / hour for the length of...
- Math - A tour boat on a river traveled 40 miles downstream in 4 hours. The ...
- Word Problems!! - PLz help me!These questions are on my study guide for ...