Question

A motor boat takes 2 hours to travel a distance 9 km down the current; and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hr) respectively are
A. 3, 1.5
B. 3, 2
C. 3.5, 2.5
D. 3, 1

Answer 1

Hint: In order to solve the problem first find out the speed of the boat and the current for the problem first find out the upstream speed and the downstream speed of the boat respectively and then use the formula which gives the relation between speed of the boat, current in terms of upstream and downstream speed.

Complete step-by-step answer:

As we know the general formula for the speed is given by,
$ \Rightarrow {\text{speed}} = \dfrac{{{\text{distance covered}}}}{{{\text{time taken}}}}$
Let us find out the speed of the boat upstream and downstream by the help of a problem statement.
Let us find out upstream speed:
$
   \Rightarrow {\text{upstream speed}} = \dfrac{{{\text{distance covered}}}}{{{\text{time taken}}}} \\
   \Rightarrow {\text{upstream speed}} = \dfrac{{9km}}{{6hr}} \\
   \Rightarrow {\text{upstream speed}} = 1.5km/hr \\
 $
Now, let us find out downstream speed:
$
   \Rightarrow {\text{downstream speed}} = \dfrac{{{\text{distance covered}}}}{{{\text{time taken}}}} \\
   \Rightarrow {\text{downstream speed}} = \dfrac{{9km}}{{2hr}} \\
   \Rightarrow {\text{downstream speed}} = 4.5km/hr \\
 $
As we know that the formula for the speed of the boat in the still water is given by:
$ \Rightarrow {\text{speed of the boat}} = \dfrac{{{\text{upstream speed}} + {\text{downstream speed}}}}{2}$
Now let us substitute the value of the upstream speed and the downstream speed in order to find the speed of the boat.
$
   \Rightarrow {\text{speed of the boat}} = \dfrac{{4.5 + 1.5}}{2}km/hr \\
   \Rightarrow {\text{speed of the boat}} = \dfrac{6}{2}km/hr \\
   \Rightarrow {\text{speed of the boat}} = 3km/hr \\
 $
Also we know that the formula for the speed of the current in terms of upstream and downstream speed is given by:
$ \Rightarrow {\text{speed of the current}} = \dfrac{{{\text{downstream speed}} - {\text{upstream speed}}}}{2}$
Now let us substitute the value of the upstream speed and the downstream speed in order to find the speed of the current.
$
   \Rightarrow {\text{speed of the current}} = \dfrac{{4.5 - 1.5}}{2}km/hr \\
   \Rightarrow {\text{speed of the current}} = \dfrac{3}{2}km/hr \\
   \Rightarrow {\text{speed of the current}} = 1.5km/hr \\
 $
Hence, the speed of the boat in the still water is 3 km/hr and the speed of the current is 1.5 km/hr.

So, option A is the correct option.

Note: In order to solve such problems students must remember the relations or the formulas connecting the boat speed and the downstream, upstream speed. Students must visualize that whenever the boat goes downstream, the current of the water supports the boat and increases its speed and while going upstream the water current opposes the boat and hence the upstream speed is always lower than downstream speed.