A motor boat whose speed is 18km/h, takes one hour more to go 24km upstream than to return down stream to the same spot. Find the speed of the boat
Answers
Answer:
let the speed of the stream be x km/hr.
therefore,the speed of the boat upstream =(18–x)km/hr and the speed of the boat downstream =(18+x)km/hr.
the time taken to go upstream=distance/speed=
24/18-X hrs
similarly,the time taken to go downstream =
24/18-x
according to the question,
24/18-x – 24/18+x=1
24(18+x)-24(18-X)=(18-X)(18+x)
x²+48x-324=0
Answer is x=6 or x= -54
Solution: Let speed of stream be x km/h
Remember these points
- Upstream: 18 - x km/h
- Downstream: 18 + x km/h
- Time = Distance/Speed
Time Taken by;
Upstream = 1 hr more than Downstream
→ 24/(18 - x) = 24/(18 + x) + 1
→ 24/(18 - x) - 24/(18 + x) = 1
→ 24[1/(18 - x) - 1/(18 + x)] = 1
→ 24[(18 + x - 18 + x)/(324 - x²)] = 1
→ 24[2x/(324 - x²)] = 1
→ 48x = 324 - x²
→ x² + 48x - 324 = 0
→ x² + 54x - 6x - 324 = 0
→ x(x + 54) - 6(x + 54) = 0
→ (x - 6)(x + 54) = 0
→ x = 6, - 54
Since speed can't be negative hence, speed of stream is 6 km/h.