HKD1710 wrote:

In a given river, the current is 6 mph. A certain riverboat can travel 18 mph in still water. How far upstream (against the current) can the boat travel if a round trip is to take 10 hours?

A) 24

B) 48

C) 60

D) 80

E) 96

Another approach: set distances equal. The boat covers the same distance on both legs of the trip.

D = r*t for each leg of the trip (r = speed)

Upstream speed: (still water speed) - (speed of current)

Downstream speed: (still water speed) + (speed of current)

Total time is 10 hours.

If one leg's time =

t, other leg's = (10 - t)

Upstream legSpeed (rate) = (18-6) = 12

Time = t

Distance = r*t = 12t

Downstream legSpeed (rate) = (18+6) = 24

Time = (10 - t)

Distance = r*t = 24(10 - t)

D = D

12t = 24(10-t)

12t = 240 - 24t

Divide by 12:

t = 20 - 2t

3t = 20

t = \(\frac{20}{3}\)

How far upstream can the boat travel? rt = D

12 * \(\frac{20}{3}\) = 80

Answer D

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