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?
Answer & explanation
Correct answer: option 3
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