Question

A boat traveled 147 miles downstream and back. The trip downstream took 7 hours. The trip back took 147 hours. Find the speed of the boat in still water and the speed of the current.

Answer 1

Answer:

The speed of boat in still water is 11 miles per hour

The speed of current is 10 miles per hour .

Step-by-step explanation:

Given as :

The distance cover by boat in downstream = $d_1$ = 147 miles

The time taken by boat in downstream trip = $t_1$ = 7 hours

The distance cover by boat in upstream = $d_2$ = 147 miles

The time taken by boat in upstream trip = $t_2$ = 147 hours

Let The speed of boat in still water =  $s_1$ = x mph

And  The speed of the current =  $s_2$ = y mph

Now, According to question

Speed = $\dfrac{\textrm Distance}{\textrm Time}$

For downstream

$s_1$ +  $s_2$ = $\dfrac{d_1}{t_1}$

or, x + y =   $\dfrac{147}{7}$

I.e x + y = 21   mph              ..........1

For upstream

$s_1$ +  $s_2$ = $\dfrac{d_2}{t_2}$

or, x - y =   $\dfrac{147}{147}$

I.e x - y = 1   mph              ..........2

Now, Solving Eq 1 and 2

I.e (x + y) + (x - y) = 21 + 1

Or, (x + x) + (y - y) = 22

Or, 2 x = 22

∴  x = $\frac{22}{2}$

I.e x = 11  mph

So, speed of boat = x = 11 miles per hour

Again, put The value of x in Eq 2

So,  x - y = 1   mph    

I.e   11 - y = 1

∴, y = 11 - 1

I.e y = 10 mph

So, speed of current = y = 10 miles per hour

Hence The speed of boat in still water is 11 miles per hour , and The speed of current is 10 miles per hour . Answer