Question

The excursion boat on the river takes 2 1/2 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? (4c)(2.5) + (6c)(2.5) = 24 (4c)(12) + (6c)(12) = 2.5 [12/(4c)] + [12/(6c)] = 2.5

Answer 1

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

Explanation:

time = distance/speed

You know the speeds upstream (5-1)c and downstream (5+1)c, the distance, and the total time for both trips. This information can be combined to give the equation above.

_____

The first equation assumes the trips upstream and down took 2.5 hours each.

The second equation is an incorrect combination of the numbers, as the units on the left are miles²/hour and are equated to hours on the right.

The third equation makes appropriate use of the relation between speed, distance, and time.

Answer 2

Last option as

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

Explanation:

Time = distance/speed

Speed of boat = 5c (given)

Hence upstream speed = 5c+c =6c and

downstream speed = 5c-c =4c

Distance remains the same 12 miles for up and down

Total time = 2.5 hours

The first equation assumes total time as 5 hours when it is actually 2.5 hours.

The second equation is an incorrect because time x distance will not yield any result instead distance /time should have been done.

The third equation calculates time taken for upstream and downstream and add to equate to 2.5 hours.

So this is correct.