Question

A boat sails downstream from point a to point b, which is 10 km away from a, and then returns to

a. if the actual speed of the boat (in still water) is 3 km/h, the trip from a to b takes 8 hours less han that from b to

a. what must the actual speed of the boat for the trip from a to b to take exactly 100 minutes?

Answer 1

Hey

Here is your answer,

Let speed of the stream
=y km/hr

Distance between A and B = 10 km

If the actual speed of the boat(in still water) is 3 km/h,
time taken to travel downstream, A to B
=10/3+y

time taken to travel upstream, B to A
=10/3−y

10/3+y=10/3−y−8
10(3−y)=10(3+y)−8(3+y)(3−y)
30−10y=30+10y−8(9−y2)
20y=8(9−y2)
5y=2(9−y2)
5y=18−2y^2
2y^2+5y−18=0
2y^2+9y−4y−18=0
y(2y+9)−2(2y+9)=0
(2y+9)(y−2)=0
y=2


Let speed of the boat needed (in still water) =x
for the trip from A to B (downstream) to take exactly 100 minutes.

Then speed downstream
=(2+x)
2+x=10/(100/60)
2+x=(10×60/100)=6
x=4

Hope it helps you!