Question

The excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current? Which of the following equations can be used to solve for c, the rate of the current?
1. (4c)(2.5) + (6c)(2.5) = 24
2.(4c)(12) + (6c)(12) = 2.5
3.[12/(4c)] + [12/(6c)] = 2.5

Answer 1

Answer:

$\dfrac{12}{4c}+\dfrac{12}{6c}=\dfrac{5}{2}$ - choice B

Step-by-step explanation:

Let c miles per hour be the rate of the river current. If the rate at which the boat travels in still water is 5 times the rate of the river current, then the rate of the boat is 5c miles per hour.

1. Upstream the rate of the boat is 5c-c=4c miles per hour. To overcome 12 miles upstream it is needed

$\dfrac{12}{4c}=\dfrac{3}{c}\ hours.$

2. Downstream the rate of the boat is 5c+c=6c miles per hour. To overcome 12 miles downstream it is needed

$\dfrac{12}{6c}=\dfrac{2}{c}\ hours.$

2. The total time is

$\dfrac{3}{c}+\dfrac{2}{c}=\dfrac{5}{c}\ hours.$

If the excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return, then

$\dfrac{5}{c}=2\dfrac{1}{2}.$

Solve this equation:

$\dfrac{5}{c}=\dfrac{5}{2},\\ \\c=2\ mi/h.$

This equation was obtained as

$\dfrac{12}{4c}+\dfrac{12}{6c}=\dfrac{5}{2}.$

Answer 2

Answer:

3.[12/(4c)] + [12/(6c)] = 2.5

Step-by-step explanation:

let,

c = current rate

And

5c = boat rate in the still water

so,

5c - c = 4c is the effective upstream speed

And

5c + c = 6c is the effective downstream speed

We write an equation for time:

time = distance/rate

up time + down time = 2.5 hrs

The equation we use to solve this is:

[12/(4c)] + [12/(6c)]= 2.5 .

now

multiply whole equation(left hand side and right hand side both) by 12c:

[12/(4c)] + [12/(6c)]*12c= 12c*(2.5)

and you will get following equation:

3(12) + 2(12) = 30c

36 + 24 = 30c

60 = 30c

c = 60/30

the rate of of the current is:

c = 2