Question

In still water, a boat averages 12 miles per hour. It takes the same amount of time to travel 14 miles downstream, with the current , as it does 7 miles upstream, against the current. What is the rate of the water's current?

Answer 1

Rate of water's current = 36 miles per hour

Explanation:

Let C be the speed of water current

Speed of still water is 12 miles per hour

We know time = distance/ speed

Down stream:

Speed on downstream =C+12

distance travelled = 14 miles

Time =
`(14)/(C+12)`

Upstream

Speed on upstream= C-12

distance travelled = 7 miles

Time =
`(7)/(C-12)`

Time taken for both upstream and down stream are equal . so equate each other and solve for C

`(14)/(C+12)=(7)/(C-12)`

cross multiply it

`14(C-12)=7(C+12)`

`14C-168=7C+84`

Subtract 7C from both sides

`7C-168=84`

Add 168 on both sides

`7C=252`

Divide both sides by 7

C= 36

Rate of water's current = 36 miles per hour

Answer 2

Down stream = Speed will be added
Up stream = Speed will be reduced

14/(12 + c) = 7/(12 - c) . ............ multiply all by 12

14 (12-c) = 7 (12 + c)

168 - 14 c = 84 + 7c

84 = 21 c

c = 4 miles/second