Respuesta :
Answer: the current of the river is 3 mph.
Step-by-step explanation:
Let x represent the current of the river.
The boat travels 2.4 miles downstream. Assuming it travelled with the current of the river. If the boat travels at an average speed of 21 miles per hour in the still water, it means that the total speed at which the boat travelled downstream is
(21 + x) mph
Time = distance/speed
Time taken to travel downstream is
2.4/(21 + x)
it travels 1.8 miles upstream. Assuming it travelled against the current of the river. it means that the total speed at which the boat travelled upstream is
(21 - x) mph
Time taken to travel upstream is
1.8/(21 - x)
Since the time taken to travel upstream and downstream is the same, then
2.4/(21 + x) = 1.8/(21 - x)
Cross multiplying, it becomes
2.4(21 - x) = 1.8(21 + x)
50.4 - 2.4x = 37.8 + 1.8x
2.4x + 1.8x = 50.4 - 37.8
4.2x = 12.6
x = 12.6/4.2
x = 3 mph
Answer and Step-by-step explanation:
[tex]Greetings![/tex]
[tex]Let's~answer~your~question![/tex]
[tex]Let~ x ~miles~ per~ hour~ be ~the~ current~ of~ the~ river.[/tex]
1. The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour. It takes him
[tex]\frac{2.4}{21+x}~hours[/tex]
2. The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour. It takes him
[tex]\frac{1.8}{21-x}~hours[/tex]
3. The time is the same,so:
[tex]\frac{2.4}{21+x} =\frac{1.8}{21-x}[/tex]
[tex]Now,~cross~multiply:[/tex]
[tex]2.4(21-x)=1.8(21+x)[/tex]
[tex]Multiply~by~10~now:[/tex]
[tex]24(21-x)=1.8(21+x)[/tex]
[tex]Divide~by~6:[/tex]
[tex]4(21-x)=3(21+x)[/tex]
[tex]84-4x=63+3x[/tex]
[tex]84-63=3x+4x[/tex]
[tex]7x=21[/tex]
[tex]x=3[/tex]
Thus, 3 miles per hour is your answer to the question.
