Question

irena’s boat traveled 76 miles downstream in 4 hours. on the way back it took her 5 hours and 30 minutes to travel 38.5 miles. 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:

The speed of the boat in still water is 13 miles/hour.

The speed of the current is 6 miles/hour.

Step-by-step explanation:

Let the speed of the boat in still water be x

And speed of the current be  y

As we know $speed=\frac{distance}{time}$

$speed=\frac{76}{4}$

$\Rightarrow speed=19$

So, since boat travelled downstream

x+y=19         (a)

Time taken by boat = 5 hours and 30 min = 5.5 hours (1 hour = 60 min)

$speed=\frac{38.5}{5.5}=7$

Traveling upstream speed of the boat will be :

x-y=7         (b)

On Solving both equations (a)and (b).

Substituting value of x in (b) equation we get:

19-y-y=7

-2y=-12

y=6

Now, substituting  value of y=6 in (a) equation:

x+6=19

x=13

The speed of the boat in still water is 13 miles/hour.

And speed of current will be 6 miles/hour.

Answer 2

Answer:

The speed of the boat in still water is 13 miles/hour.

The speed of the current is 6 miles/hour.

Step-by-step explanation:

Let the speed of the boat in still water be x

And speed of the current be  y

When Irena's travelling downstream, the speed of the boat is:

$Speed=\frac{76 miles}{4 hours}=19 miles/hour$

Traveling down stream the speed of the boat will be :

$x+y=19$..(1)

When Irena's travelling upstream, the speed of the boat is:

Time taken by boat = 5 hours and 30 min = 5.5 hours (1 hour = 60 min)

$Speed=\frac{38.5 miles}{5.5 hours hours}=7 miles/hour$

Traveling down stream the peed of the boat will be :

$x-y=7$..(2)

On Solving both equation (1)and (2).

$x+y=19$

$x=19-y$ putting value of x in (2) equation

$19-y-y=7$

y = 6 miles/hour

Putting value of y in (1) equation:

$x+6=19$ , x = 13 miles/hour

The speed of the boat in still water is 13 miles/hour.

The speed of the current is 6 miles/hour.