Question

a boat can cover a distance of 7.2 km downstream and 3.2km upstream in 2 hrs.It can also cover 1.5km downstream and 0.6km upstream in 24 minutes.What is the speed of the boat when going downstream(in km/hr) ?

Answer 1

Answer:

Speed downstream is (x+y) km/hr

Answer 2

The speed of the boat when going downstream is 6 km/h.

Step-by-step explanation:

Let the speed of boat in downstream be 'x' and speed in upstream be 'y'.

Case 1:

Now, Distance covered in downstream is, $D_d=7.2\ km$

Distance covered in upstream is, $D_u=3.2\ km$

Now, Time taken for downstream distance is given as:

$t_d=\frac{D_d}{x}\\t_d=\frac{7.2}{x}---1$

Time taken for upstream distance is given as:

$t_u=\frac{D_u}{y}\\t_u=\frac{3.2}{y}----2$

Now, total time taken is 2 hours. Therefore,

$t_d+t_u=2\\\frac{7.2}{x}+\frac{3.2}{y}=2---3$

Case 2:

Now, Distance covered in downstream is, $D_d=1.5\ km$

Distance covered in upstream is, $D_u=0.6\ km$

Now, Time taken for downstream distance is given as:

$t_d=\frac{D_d}{x}\\t_d=\frac{1.5}{x}---4$

Time taken for upstream distance is given as:

$t_u=\frac{D_u}{y}\\t_u=\frac{0.6}{y}----5$

Now, total time taken is 24 minutes which is equal to $\frac{24}{60}$ hours. Therefore,

$t_d+t_u=\frac{24}{60}\\\frac{1.5}{x}+\frac{0.6}{y}=0.4---6$

Solving equations (3) and (6) for 'x' and 'y', we get:

$x=6\ and\ y=4$

Therefore, speed of boat in downstream is 6 km/h.