(Q11)A motor boat whose speed is 18 km/h in still water.It takes 1 hour more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer:

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 - x)km/h and the speed of the boat downstream = (18 + x)km/h.

The time taken to go upstream =
distance
speed
 =
24
18-x
 hours.
Similarly, the time taken to go downstream =
24
18 + x
 hours.
According to the question,
24
18 - x
 -
24
18 + x
 = 1

i.e 24(18 + x) - 24(18 - x) = (18 - x)(18 + x)

i.e x2 + 48x - 324 = 0

Using the quadratic formula, we get

x =
-48±√482+√
2
 =
-48±√
2
=
-48±
2
= or -54

Since x is the speed of the stream, it cannot be negative. So,we ignore the root x= -54.

Therefore, x= gives the speed of the stream as km/h.