The speed of a boat in still water is 15 km/h. It can go 30km upstream and return downstream to the original point in 4h and 30min. Find the speed of stream.
Answers
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Time taken to go 30 km upstream = 30/(15 - x) hrs. Time taken to go 30 km downstream = 30/(15 + x) hrs. Hence, the speed of stream is 5 km/h.
Answer:
5 km/h
Step-by-step explanation:
Let the speed of the train be x km/h.
Downstream speed = (15 + x) km/h
Upstream speed = (15 - x) km/h
Time taken to go 30 km upstream = 30/(15 - x) hrs.
Time taken to go 30 km downstream = 30/(15 + x) hrs.
According to the Question,
⇒ 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
By cross-multiplication, we get
⇒ 9(225 - x²) = 1800
⇒ 225 - x² = 200
⇒ x² = 25
⇒ x = ± 5
(As speed can't be negative)
⇒ x = 5 km/h
Hence, the speed of stream is 5 km/h.