Answer:
2 km/h
Step-by-step explanation:
You can make a rate-time-distance chart to help you figure it out.
| R | D | T
MB | 12-x | 25 | 25/(12-x)
Raft | x | 25 | 25/x
This means that the speed of the current in this case is x. The speed of the raft is also x because it is traveling with the current. The speed of the motorboat would be 12-x because you have to factor in the current. The time for both of them is the distance divided by the speed.
You also have another relationship that you know about. You know that the time it takes to travel by raft is 10 more than the time it takes to travel by motorboat. This means that to make 25/(12-x) and 25/x equal you would need to add ten to the 25/(12-x)
This gives you the equation:
25/(12-x) + 10 = 25/x
From there you can start solving
(25+120-10x)/(12-x)=25/x
Then you cross multiply and get:
300-25x=145x-10x^2
Then you put everything to one side and get:
10x^2-170x+300=0
Then you factor out the 10 and get:
10(x^2-17x+30)=0
Then you can factor x^2-17x+30 and get (x-2)(x-15)
From there you can apply the zero product property and say that
x-2=0
x=2
And that
x-15=0
x=15
Now you have two solutions but the answer can't be 15 because if you do 12-15 to find the speed of the motorboat you would get a negative number and speed cannot be negative. Therefore the only possible answer is 2.
Hope this helps and let me know if something doesn't make sense in my solution!
