Question

2. A motorboat travels 30 min upstream against a 4-mph current. Returning with current takes 18 min. Find the speed of the motorboat in still water (6pts) (d = rt) Rate Time Distance=rt Upstream Downstream 3. Find an equation of the line containing the point(3,-5) and perpendicular to the line 3x - 5y = 9 (5pts)

Answer 1

2)

Let, speed of motorboat in still water is k mph

Then for upstream rate is (k-4) mph & for returning rate is (k+4) mph.

So, for going in 30 minutes it goes 30(k-4)/60 mile = (k-4)/2 mile

For returning in 18 minutes it goes 18(k+4)/60 mile = 3(k+4)/10 mile

Accordingly , (k-4)/2 = 3(k+4)/10

Or, 10k - 40 = 6k + 24

Or, 4k = 64

Or, k = 16

So, speed of motorboat in still water is 16 mph.

So, rate in upstream is 12 mph and downstream is 20 mph.

Upstream take 30 minutes and downstream takes 18 minutes

Both cover the distance 6 mile. ( By putting k value in upstreams and downstream goes distance).

upstream Time Distance Rate 12 mph 30 min Downstream 6 m 20 mph 18 min 6 m scannea wun camscanner CS