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Katarina
6 days ago
11

A small boat traveled 29.5 miles upstream in 2 hours. The same boat took 3 hours to travel 59.25 miles downstream. If the speed

and direction of the water was the same in both directions, find the speed of the boat in still water and the speed of the current.
Mathematics
1 answer:
PIT_PIT [9.1K]6 days ago
5 0

Answer:

  • Boat speed: 17.25 mph
  • Current: 2.5 mph

Step-by-step explanation:

When going upstream, the current's speed (c) reduces the boat's speed (b), resulting in a net speed. Conversely, going downstream, the current's speed adds to the boat's speed. We can use the relation...

speed = distance/time

b - c = 29.5/2 = 14.75..... miles/hour

b + c = 59.25/3 = 19.75....miles/hour

By subtracting the first equation from the second, we arrive at...

(b+c) - (b-c) = 19.75 - 14.75

2c = 5

c = 2.5

Then we can use any of the equations to calculate b:

b = 14.75 + c = 17.25

The boat's speed in still water amounts to 17.25 miles per hour, while the current's speed is 2.5 miles per hour.

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