# A boat can travel on a river 15 miles upstream in the same time it takes to travel 23 downstream. Find the spe?

A boat can travel on a river 15 miles upstream in the same time it takes to travel 23 downstream. Find the speed of the current if the speed of the boat in still water is 19 miles per hour.

Relevance

subtract the current speed (x) from 19 mph on the "upstream" side of the equation, and add it to the "downstream" so it'll look something like this.

15miles/(19-x)=23miles(19+x)

just solve for x (I got 4mph, but you should double check that)

• time = (distance)/(speed)

Let the current be "x" mph.

Upstream travel velocity = boat velocity in still water -current velocity = (19-x) as the current tries to carry it downstream.

So Upstream travel time = 15/(19-x)

down stream travel velocity = boat velocity in still water + current velocity = (19+x) as the current speeds it up downstream.

So Upstream travel time = 23/(19-x)

Now the times are equal so

15/(19-x) = 23/(19-x)

solving for "x" by cross multiplication and getting the x terms in one side, we get,

x = 4 mph.

Check: upstream boat speed 19-4 = 15 mph, it takes 1 hour to cover 15 miles.

downstream boat speed = 19 + 4 = 23 mph, it takes the same 1 hour to travel 23 miles.