SOLUTION: A kayak wint up a river and back in 6 hours. If their rate up the river was 2 miles per hour and back 4 miles per hour, how far did they go up the river?
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Question 83155: A kayak wint up a river and back in 6 hours. If their rate up the river was 2 miles per hour and back 4 miles per hour, how far did they go up the river? Found 2 solutions by Mogana, JDorrin:Answer by Mogana(4) (Show Source):
You can put this solution on YOUR website! Let x be time taken upstream and y time taken downstream.
Total number of hours is: x + y = 6hrs
Given speed upstream is 2miles per hour and speed downstream is 4 miles per hour.
the distance traveled upstream = distance traveled downstream
==>speed upstream * time taken = speed downstream * time taken
2 *x = 4 * y
Substitute for y in the above
2 * x = 4 * (6-x)
2(x) = 24 - 4x
6x = 24
x = 24 /6
x = 4hrs
The time taken upstream is 4hrs
we know that..
distance traveled upstream = speed upstream * time taken
= 2 * 4 = 8 miles
You can put this solution on YOUR website! since the kayak goes one directions 2mph and the other direction 4 mph, it is known that the kayak goes twice the speed on the way back, so it takes half the time. It is also known that the kayak is traveling for 6 hours. Therefore, the kayak spends twice as much time going up than coming back.
2x+x=6hours x=2
The kayak spends 2x, or 4 hours, going up and x, or 2, hours coming back
Traveling 4 hours at 2 mph will equal 8 miles
Traveling 2 hours at 4 mph will equal 8 miles
The kayak travels a total of 8 miles up the river and 8 miles back
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