Question

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.

Answer 1

Answer:

• boat speed: 17.25 mph
• current: 2.5 mph

Step-by-step explanation:

Upstream, the speed of the current (c) subtracts from the speed of the boat (b) to give the net speed. Downstream, the speed of the current adds. We can make use of the relation ...

  speed = distance/time

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

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

Subtracting the first equation from the second, we get ...

  (b+c) -(b-c) = 19.75 -14.75

  2c = 5

  c = 2.5

Then either equation can be used to find b:

  b = 14.75 +c = 17.25

The speed of the boat in still water is 17.25 miles per hour; the speed of the current is 2.5 miles per hour.