Question 926420

My friend Ken will drive a boat. 


Step 2:
Select a current speed of the water in mph.

Speed of current will be {{{7mph}}}.


Step 3:
Select the number of hours (be reasonable please) that your friend or family member drove the boat or jets ski against the current speed you chose in step 2.

Ken will drive the boat upstream {{{60}}} miles in {{{6}}} hours.


Step 4:
Select the number of hours that your friend or family member made the same trip with the current (this should be a smaller number, as your friend or family member will be traveling with the current).

Ken will drive the boat downstream {{{72}}} miles in {{{3}}} hours. 


Step 5:
Write out the word problem you created and calculate how fast your friend or family member was traveling in still water. Round your answer to the nearest mph.


Ken wanted to try out his new boat so he parked his car and a friend drove him to the marina where he took possession of his boat. He drove the boat upstream 60 miles for {{{6}}} hours and then back downstream {{{72}}} miles (to where his car with boat carrier was parked) in {{{3}}} hours. What was the speed of the boat in still water?


Solution: 

Let {{{C}}} mph equal the Current of the river and {{{b}}} mph the rate of the boat.

Remember that {{{d = st}}} (distance = speed * time)

Upstream: 

{{{60 = 6(b-c)}}}
Downstream: {{{72 = 3(b+c)}}}

So we have two equations:

{{{60 = 6b - 6c}}}
{{{72 = 3b + 3c}}}
_______________________

Solve both equations for {{{b}}}:

{{{b = 10 + c}}}
{{{b = 24 - c}}}
_________________________

Now set equal to each other and solve for {{{c}}}:

{{{10 + c = 24 - c}}}

{{{2c = 14}}}

{{{c = 7mph}}}

So the speed of the current was {{{7mph}}}  

Now plug this into either of the original equations to find the speed of the boat in still water.

We will choose the first one:

{{{b = 10 + c}}}

{{{b = 10 + 7}}}

{{{b = 17}}}

The speed of the boat in still water was {{{17mph}}}.