A boat can travel 8 mph in still water. If it can travel 15 miles downstream in the same time that it can travel 9 miles up the stream, what is the rate of the stream?

1 Answer
Jul 29, 2016

#9 1/7" miles per hour"#

Explanation:

Let the time of travel in each direction be #t#

Let the velocity of the water be #v#

Let distance be #s#

Given that the boat velocity is 8 mph

Downstream #-> s= (8+v)t=15#.....................Equation(1)

Upstream # -> s=(8-v)t=9#...........................Equation(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write Eqn(1) as: #8t+vt=15 .........................................(1_a)#
Write Eqn(2) as: #8t-vt=9.........................................(2_a)#

#Eqn(1_a)+Eqn(2_a)# gives:

#16t=14 => t=14/16 -=7/8#.............................(3)

Using #Eqn(3)# substitute for #t# in #Eqn(1_a)#

(This should work no matter which equation you choose)

#color(brown)(8t+vt=15)color(blue)(" "->" "8(7/8)+v(7/8)=15#

#v=8/7(15-7) = 64/7" "("miles")/("hour")#