SOLUTION: Your help is greatly appreciated. Here is my problem: A boy can drive a motorboat 45 miles downstream in the same amount of time that he can drive 27 miles upstream. Wh

Question 6314: Your help is greatly appreciated. Here is my problem:
A boy can drive a motorboat 45 miles downstream in the same amount of time that he can drive 27 miles upstream. What is the speed of the current in the river if the speed of the boat in still water is 12 mph
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!
A boy can drive a motorboat 45 miles downstream in the same amount
of time that he can drive 27 miles upstream. What is the speed of
the current in the river if the speed of the boat in still water
is 12 mph.
`
Let x = the speed of the current.
Make a DRT chart
`
` ` ` ` ` `|`Distance | Rate `| ` Time `
downstream | ` ` ` ` `|` ` ` `| ` ` ` ``
upstream ` | ` ` ` ` `|` ` ` `| ` ` ` ``
`
Fill in the given distances
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|` ` ` `|` ` ` ` ``
upstream ` | ` `27 ` `|` ` ` `|` ` ` ` ``
`
Now fill in the rates. The rate downstream is the sum of the rate of
the boat if in still water + the rate of the current, or 12+x. The rate
upstream is the difference of the rate of the boat if in still water -
the rate of the current, or 12-x.
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|`12+x `|` ` ` ` ``
upstream ` | ` `27 ` `|`12-x `|` ` ` ` ``
`
Now fill in the times using Time = Distance/Rate
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|`12+x `| 45/(12+x)
upstream ` | ` `27 ` `|`12-x `| 27/(12-x)
`
>>...downstream in the same amount of time...upstream...<<
`
The key words are "same amount of time". "Same" means "equal", so
we set the two times equal to each other
`
` ` ` ` ` ` ` ` `
`
Can you solve this equation? If not post again.
`
` ` ` ` ` ` ` ` ` Answer: x = 3 mph.
`
Checking: This means the boat never went 12 mph because there
was no still water. It went 15 mph upstream and 9 mph downstream.
The time to go 45 miles downstream at 15 mph was 3 hours. The time
to go 27 miles upstream at 9 mph was also 3 hours.
`
Edwin J

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