Word problems

[rachelmaddie]

Hi, can someone please check this for me?

The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour.
Let x miles per hour represent the current of the river.
2.4/21 + x hours

The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour.
1.8/21 - x hours

The time is the same in the equation
2.4/21 + x = 1.8/21 - x

Cross multiply:
2.4(21 - x) = 1.8(21 + x)

Multiply by 10:
24(21 - x) = 18(21 + x)

Divide by 6:
4(21 - x) = 3(21 + x)
84 - 4x = 63 + 3x
84 - 63 = 3x + 4x
7x = 21
x = 3 mph

Solution: 3 miles per hour

 

[lev888]

Hi, can someone please check this for me?
View attachment 20602
The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour.
Let x miles per hour represent the current of the river.
2.4/21 + x hours

The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour.
1.8/21 - x hours

The time is the same in the equation
2.4/21 + x = 1.8/21 - x

Cross multiply:
2.4(21 - x) = 1.8(21 + x)

Multiply by 10:
24(21 - x) = 18(21 + x)

Divide by 6:
4(21 - x) = 3(21 + x)
84 - 4x = 63 + 3x
84 - 63 = 3x + 4x
7x = 21
x = 3 mph

Solution: 3 miles per hour

Your explanation is not clear.
1. "Let x represent" should come _before_ you use x in an expression.
2. You state that x is speed, yet you write "x hours"
3. Any expression should be preceded by _what_ you are expressing (e.g. what is 2.4/21 + x hours?)

 

[Deleted member 4993]

Hi, can someone please check this for me?
View attachment 20602
The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour.
Let x miles per hour represent the current of the river.

2.4/21 + x hours.............................................................................................................. Incorrect. That should be 2.4/(21 + x)

The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour.
1.8/21 - x hours

The time is the same in the equation
2.4/21 + x = 1.8/21 - x .............................................................................................................. Incorrect. That should be 1.8/(21 - x)

Cross multiply:
2.4(21 - x) = 1.8(21 + x)

Multiply by 10:
24(21 - x) = 18(21 + x)

Divide by 6:
4(21 - x) = 3(21 + x)
84 - 4x = 63 + 3x
84 - 63 = 3x + 4x
7x = 21
x = 3 mph.................................................................................correct

Solution: 3 miles per hour

 

[rachelmaddie]

2.4/21 + x hours.............................................................................................................. Incorrect. That should be 2.4/(21 + x)

The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour.
1.8/21 - x hours

The time is the same in the equation
2.4/21 + x = 1.8/21 - x .............................................................................................................. Incorrect. That should be 1.8/(21 - x)

Cross multiply:
2.4(21 - x) = 1.8(21 + x)

Multiply by 10:
24(21 - x) = 18(21 + x)

Divide by 6:
4(21 - x) = 3(21 + x)
84 - 4x = 63 + 3x
84 - 63 = 3x + 4x
7x = 21
x = 3 mph.................................................................................correct

Solution: 3 miles per hour

Let x miles per hour represent the current of the river.
The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour.

2.4/(21 + x) hours

The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour.
1.8/(21 - x) hours

The time is the same in the equation
2.4/(21 + x) = 1.8/(21 - x)

Cross multiply:
2.4(21 - x) = 1.8(21 + x)

Like this?

 

[rachelmaddie]

Your explanation is not clear.
1. "Let x represent" should come _before_ you use x in an expression.
2. You state that x is speed, yet you write "x hours"
3. Any expression should be preceded by _what_ you are expressing (e.g. what is 2.4/21 + x hours?)

How do I correct it?

 

[lev888]

How do I correct it?

I don't understand your question. I didn't just say your answer was incorrect. I pointed out exactly what in your explanation needed attention.

 

[rachelmaddie]

I don't understand your question. I didn't just say your answer was incorrect. I pointed out exactly what in your explanation needed attention.

Yes, I meant can you show me what I need corrected in my explanation?

 

[lev888]

Yes, I meant can you show me what I need corrected in my explanation?

I pointed out exactly what in your explanation needed attention. E.g. what in the first item is not clear?

 

[rachelmaddie]

I pointed out exactly what in your explanation needed attention. E.g. what in the first item is not clear?

I don’t understand what you mean in 2 and 3.

 

[lev888]

I don’t understand what you mean in 2 and 3.

2. 2.4/21 + x hours is confusing because, as I wrote in 3., you don't tell us what the expression means. It looks like you are adding x hours to something, but x is speed, not time. It turns out it should've been 2.4/(21 + x), which makes a bit clearer that hours doesn't refer to x.
3. What would make it even more clear is telling us that the expression above refers to _time_ of the downstream trip. Now we understand that hours refers to the units of the whole expression. Same for the second expression. I would write it like this:
The time of the downstream trip is its distance over speed: 2.4/(21 + x) hours.