# A boat can travel on a river 14 miles upstream in the same time it takes to travel 24 downstream. Find the spe?

A boat can travel on a river 14 miles upstream in the same time it takes to travel 24 downstream. Find the speed of the current if the speed of the boat in still water is 19 miles per hour.

Relevance

the speed of boat in still water u = 19 mile/hour

let the speed of the current = v mile/hour

so

speed of boat in up stream = u - v miles/ hour

.......................................= 19 - v mile/ hour

speed of boat in down stream = u+v mile/hour

...........................................= u - v mile/hour

let the time taken be ' t ' in both cases

distance traveled in upstream = 14 miles

then t = 14 / ( u - v )

=> t = 14 / ( 19 - v ) ................ ( 1 )

distance traveled in downstream = 24 miles

then t = 24 / ( u + v )

=> t = 24 / ( 19 + v ) ..................( 2 )

from equation ( 1 ) and ( 2 )

14 / ( 19 - v ) = 24 / ( 19 + v )

7 ( 19 + v ) = 12 ( 19 - v )

133 + 7v = 228 - 12 v

19v = 95

=> v = 5 mile/hour

therefore speed of boat in still water = 5 mile/hour

• time = distance / speed

speed upstream = 19 - c (c = speed of current)

time upstream = 14 / (19 - c)

speed downstream: 19 + c

time downstream = 24 / (19 + c)

by inspection, the speed of the current is 5 mph, and the time traveled is 1 hour, but let's confirm that

24 / (19 + c) = 14 / (19 - c)

cross-multiply:

14(19 + c) = 24(19 - c)

266 + 14c = 456 - 24c

38c = 190

c = 190 / 38 = 5

current is 5 mph

• 2. Six pears and 3 apples fee \$3.ninety. 2 pears and 5 apples fee \$3.30. How plenty does one pear fee? including the two: 8p + 8a = 7.20 => 1p + 1a = 0.ninety Subtraction => 4p - 2a = 0.60 => 2p - 1a = 0.30. including 3p = a million.20 => 1p = \$0.40