# Math question.................?

Hi! I'm having some trouble with this math problem, if you answer, please make sure to include how you solved it (I suck at these types of questions).

It took a boat 6H to travel 84km up a river against the current but only 4H and 12 minutes for the return trip with the current. Find the speed of the boat in still water and the speed of the current.

Thanks!

Relevance
• Anonymous
9 years ago

Mark your boat speed as B and your current speed as C.

Then your boat speed traveling against the current would be:

B = 84/6 - C (minus current speed)

Traveling with current it would be:

B = 84/4.2 + C (plus current speed. And 4.2 is because 12 minutes is one fifth (1/5) of an hour. And 1/5 = 0.2. So 4 h and 12 min = 4.2 h)

Now you have two equations with two variables. Solve this as an equation system:

B = 84/6 - C

B = 84/4.2 + C;

Or

B = 14 - C;

B = 20 + C;

Take the first B and put in the second equation:

14 - C = 20 + C

-2C = 6;

C = -3 (minus, because it's against the boat speed).

Take this in any expression of B, for example:

B = 20 + C, because C = -3, then:

B = 20 - 3 = 17.

The answer is: Boat speed is 17km/h in still water. Current speed is 3km/h.

• Anonymous
9 years ago

Let x be the boat speed if no river current. Let y be speed of the current.

Traveling against the river, speed is x-y.

Traveling with the river, speed is x+y.

Stop, and think how those make sense.

Trip against the river: rate is 84/6 kilometers per hour. This means x-y = 84/6.

Trip with the river: 12 minutes is one fifth of an hour, which is 0.2 hours, so lets just say travel time here is 4.2 hours. Notice you already know the distance going with the river, since it is the same distance as used going against the river. Now, (x+y)(4.2)=84.

See, you now have two equations, and two variables, this system:

x-y = 84/6 and (x+y)(4.2)=84

• 9 years ago

Let the speed of boat in still water be x km / hour

And speed of current be y km / hour

UPSTREAM

84 / x -y = 6

6x -6y = 84

x - y = 14 (A)

DOWNSTREAM

84 / ( x+y) = 41/5 hours = 4.2 hours

4.2x + 4.2y = 84

x + y = 20 (B)

2x = 34

x = 17 km/ hour