A kayak can travel 24 miles downstream in 3 hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current?

Question

A kayak can travel 24 miles downstream in 3 ​hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current?

Kennedy Adams · Accepted Answer

Kayak: #5mph#

Current: #3mph# The equation you need to know is #d=rt#. However, there are two things moving: the kayak and the current. Let #k# be the speed of the kayak in still water and #c# be the speed of the current. When traveling downstream, the two speeds add. That is: #d=(k+c)t_(down)# #24=3(k+c)# #8=k+c# When traveling upstream, however, the current opposes the kayak speed so it subtracts. #d=(k-c)t_(up)# #24=12(k-c)# #2=k-c# Now, we can add the two equations to get: #8+2=(k+c)+(k-c)# #10=2k# #k=5# So, the kayak travels #5 mph#. We can plug this back into one of our other equations to get #c=3#. So, the speed of the current is #3mph#.

Jace Anderson · Answer

undefined Let the speed of the kayak in still water be $ k $ miles per hour and the speed of the current be $ c $ miles per hour.

Given:
Downstream speed = $ k + c $ miles per hour
Upstream speed = $ k - c $ miles per hour

Given that the kayak can travel 24 miles downstream in 3 hours, we have the equation:
$$ 24 = 3(k + c) $$

And given that it would take 12 hours to make the same trip upstream, we have the equation:
$$ 24 = 12(k - c) $$

Solve these two equations simultaneously to find the values of $ k $ and $ c $.

A kayak can travel 24 miles downstream in 3 ​hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current?

A kayak can travel 24 miles downstream in 3 hours, while it would take 12 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current?