Question

A boat traveled 30 km downstream in 3 hours and made the upstream trip in 5 hours. Find the speed of the boat in still water.

• A. 8 km/hr
• B. 12 km/hr
• C. 6 km/hr
• D. 10 km/hr

Answer 1

Answer: (A)

8 km/hr

Traveling downstream, the speed of the boat will be faster than it would be in still water. Traveling upstream, the speed of the boat will be less than that what it would be in still water.
We can let's represent the speed of the boat in still water and c the speed of the current. Then the rate of the boat going downstream is s + c, and its rate going upstream is s - c.
Because $d=r.t$
$3(s+c)=30$ ...... (1)
$5(s-c)=30$ ...... (2)
To solve this system by addition, we multiply, eq. (1) by 5, eq. (2) by 3, add the equations, and solve for s.
$15s+15c=150$
$15s-15c=90$
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$30s=240\Rightarrow s=8$
The speed of the boat in still water is $8$ km per hour.