Speed of river current is 6mph.Ferry operator wants to buy new boat. Every day his route takes him 22.5 miles against the current and back to his dock and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator's needs?

Question

Speed of river current is 6mph.Ferry operator wants to buy new boat.  Every day his route takes him 22.5 miles against the current and back to his dock and he needs to make this trip in a total of 9 hours.  He has a boat in mind, but he can only test it on a lake where there is no current.  How fast must the boat go on the lake in order for it to serve the ferry operator's needs?

tkhunny · Answer

Distance = Rate * Time

Distance Up = Distance Down

Rate Up = Boat Speed less River Current

Rate Down = Boat Speed plus River Current

Time Up + Time Down = 9 hours

Go!  Let's see what you get.

anonymous · Answer

is distance up half of 22.5 or is that the distance up and then the distance down

tkhunny · Answer

Whoops!  Forgot to write that.

Distance Up = Distance Down = 22.5 Miles

anonymous · Answer

so dist. up is 11.25 and down is 11.25?

tkhunny · Answer

Well, that's how I read it.  "22.5 miles against the current ".  If we don't get things as expected, we can decide that;s the WHOLE trip, rather than half the trip.

tkhunny · Answer

Distance Up = Distance Down = 22.5 Miles

This is a 45 mile trip.

anonymous · Answer

that's how I am reading it that 22.5 is round trip

anonymous · Answer

but now u are saying round trip is 45 miles

tkhunny · Answer

Let's do it both ways and clear up the confusion.  Are you solving with 22.5 for the whole trip and getting what an answer key says is "wrong".

anonymous · Answer

I don't have an answer key.  I will work with round trip of 45 miles.    do I know the boat speeed?

tkhunny · Answer

That's what we seek, isn't it?

anonymous · Answer

yes  rate up  22.5=9x:  x=2.5rate:  2.5mph-river current of 6 gives me a neative number.  What am I doing wrong?

anonymous · Answer

rate down=2.5 +6=8mph

tkhunny · Answer

Don't be afraid to write things down.

Trip Up

22.5 mi = (BoatSpeed - 6 mph)*(T Hours)

Trip Down

22.5 mi = (BoatSpeed + 6 mph)*((9-T) Hours)

How do you suggest we proceed given those clean and complete equations?

tkhunny · Answer

These equations should lead to a Quadratic Equation that can be factored.

Boat Speed = 9 mph or Boat Speed = -4 mph.

Get to that point.

BTW: If we use 22.5 as the total round trip, we get Boat Speed = 7.3788 mph.  I'm liking the other solution lots better.

anonymous · Answer

sorry, but I am not following.  How can a boat speed be negative 4?

tkhunny · Answer

Excellent.  You ARE following.  That is EXACTLY the question I was hoping you would ask.  Did you get the quadratic equation?  Show me, please.