A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Solution:
Let
the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.

Now,
{30/(15 + x)} + {30/(15 - x)} = 9/2
⇒ 30(15 - x) + 30(15 + x)/(15 + x)(15 - x) = 9/2
⇒ (450 - 30x + 450 + 30x)/(225 - x²) = 9/2
⇒ 900/(225 - x²) = 9/2
⇒ 100/(225 - x²) = 1/2
⇒ 200 = 225 - x²
⇒ x² = 225 - 200
⇒ x² = 25
⇒ x² = 5²
⇒ x = 5

the speed of the stream be 5 km/hr.