<PRE><B>Question 1075485</B>
A tourist traveled on a motorboat against the current for 25 km.
 And then returned back on a raft.
 In the boat the tourist traveled for 10 hours less than on the raft.
 Find the speed of the current if the speed of the motorboat in still water is 12 km/hour.
:
let c = the speed of the current (also the speed of the raft)
then
(12-c) = boat speed against the current
:
Write a time equation; time = dist/speed
raft time - boat time = 10 hrs
{{{25/c}}} - {{{25/((12-c)) = 10}}}
multiply equation by c(12-c), cancel the denominators
25(12-c) - 25c = 10c(12-c)
300 - 25c - 25c = 120c - 10c^2
300 - 50c = 120c - 10c^2
10c^2 - 50c - 120c + 300 = 0
10c^2 - 170c + 300 = 0
simplify, divide by 10
c^2 - 17c + 30 = 0
Factors to
(c-15)(c-2) = 0
Two solutions, but only one is reasonable
c = 2 km/hr is the rate of the current
:
;
Check this by finding the time each way (boat speed: 12 - 2 = 10 km/hr
25/2 = 12.5 hrs
25/10 = 2.5 hrs
-----------------
time dif: 10 hrs as given
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