Question

A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water.

Answer 1

Answer:

Speed of the boat in still water = 6.125 miles/hour

Step-by-step explanation:

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming $S_b$ to be the speed of the boat in still water and $S_w$ to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

$Speed = \frac{distance}{time}$

$S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours}$

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

$S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours}$

Adding the two equations to get:

   $S_b+S_w=\frac{d}{t_1}$

+  $S_b-S_w=\frac{d}{t_2}$

___________________________

$2S_b=\frac{d}{t_1} +\frac{d}{t_2}$

Solving this equation for $S_b$ and substituting the given values for $d,t_1, t_2$:

$S_b=\frac{(t_1+t_2)d}{2t_1t_2}$

$S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}$

$S_b=\frac{(11 hour)(33mi)}{56hour^2}$

$S_b=6.125 mi/hr$

Therefore, the speed of the boat in still water is 6.125 miles/hour.

Answer 2

Answer:

$6.48\frac{mi}{h}$

Step-by-step explanation:

Let' call "b" the speed of the boat and "c" the speed of the river.

We know that:

$V=\frac{d}{t}$

Where "V" is the speed, "d" is the distance and "t" is the time.

Then:

$d=V*t$

We know that distance traveled downstream is 33 miles and the time is 4 hours. Then, we set up the folllowing equation:

$4(b+c)=33$

For the return trip:

 $7(b-c)=33$  (Remember that in the return trip the speed of the river is opposite to the boat)

By solving thr system of equations, we get:

- Make both equations equal to each other and solve for "c".

$4(b+c)=7(b-c)\\\\4b+4c=7b-7c\\\\4c+7c=7b-4b\\\\11c=3b\\\\c=\frac{3b}{11}$

- Substitute "c" into any original equation and solve for "b":

$4b+\frac{3b}{11} =33\\\\4b+\frac{12b}{11}=33\\\\\frac{56b}{11}=33\\\\b=6.48\frac{mi}{h}$