A boat can go 40 km downstream and 25 km upstream in 7 hours 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/h) of the boat in still water?

9

We know that,

Distance = Speed × Time 

Speed in upstream = Speed of boat in still water -  Speed in current water

Speed in downstream = Speed of  boat in still water + Speed in current water 

We have,

A boat can go 40 km downstream and 25 km upstream in 7 hours30 min

48km downstream and 36 km upstream in 10 hours 

According to the question,

Let the speed of boat in still water be xkm/h and the speed current water be y km/h 

Speed in downstream = x + y , Speed in upstream = x -y 

Now, Distance/Speed = Time 

= 40/(x +y) + 25/(x -y) = 7.5 .........(1)

Also,

= 48/(x +y) + 36/(x -y) = 10 ...........(2)

Now, on multiplying eq(1) by6 and eq(2) by 5 we get

= 240/(x + y) + 150/(x -y) = 45 ............(3)

= 240/ (x +y) + 180/( x -y) = 50 .............(4) 

On eq(4) - eq(3) we get

= 30/(x -y) = 5 

= x -y = 6  ......................(5)

Now, on putting the value of x -y in eqn (2) we get

= 48/ ( x +y) + 36/6 = 10 

⇒ 48/( x + y) = 4  ⇔ x + y = 12 .............(6) 

Now, on adding eq (5) + eq (6) we gt

= 2x = 18 

= x = 9 km/h