Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

# QUESTION IS ON THE BOTTOM ! :)?

In still water, Jenna's motorboat cruises at 16.5km/h. On the river, the boat travels faster downstream than upstream,because of the current. The boat takes 5 hours for a trip upstream, but only 2 hours to cover the same distance on the return trip downstream. Determine the speed of the current.

Relevance

distance = rate * time

and the distance for upstream and downstream trips is the same,

so the products of rate and time for each trip must be the same, too.

We know the times for each case, and we know one component of each rate.

If c represents the speed of the current (in km/h, of course), then

16.5 - c is the upstream rate and

16.5 + c is the downstream rate.

This gives us the equation

(16.5 + c) 2 = (16.5 - c) 5 which we can simplify and solve for c:

33 + 2c = 82.5 - 5c

7c = 49.5

c = 49.5/7 = about 7.07 km/h

The trip upstream is at 16.5 - 7.07 = 9.43 km/h, covering 47.15 km in 5 hours.

The trip downstream is at 16.5 + 7.07 = 23.57 km/h, covering the same distance in about 2 hours.