Rate problem

Question

A canoe race team can paddle upstream 20 miles on a river in 4 hours and back down to their starting point in 2.5 hours. Determine what the speed of the river current is and the canoeing speed in still water.

Answer 1

Hi Naomi!

 

We first have to realize that distance = (rate)(time) or  d = rt.

 

Now lets name some variables.

Let the canoeing speed in still water be B and let the rate of the current be C.

When going upstream, the canoe fights the current so the rate is B - C

When going downstream, the canoe gets a boost from the current so the rate is B + C

 

 

 

UPSTREAM

d=rt

20=r(4)

5=r

So, B - C = 5

 

DOWNSTREAM

d=rt

20=r(2.5)

8=r

So, B + C = 8

 

 

Add these two equations together:

B - C = 5

B + C = 8

 

2B = 13

B = 6.5   (The boat speed is 6.5 mph)

 

Substitute this value into B + C = 8 and 

6.5 + C = 8

C = 1.5 mph

 

Hope this helps!