A boat goes 20 km against the stream and 32 km along the stream in 8 hours. It also goes 32 km against the stream and 20 km along the stream in 8.5 hours. What is the rate of stream?
Let the rate of upstream be x kmph and rate of downstream be y kmph
⇒ Then, $(\frac{{20}}{x}\; + \;\frac{{32}}{y} = 8)$ .....(1)
⇒ Also, $(\frac{{32}}{x}\; + \;\frac{{20}}{y} = \frac{{17}}{2})$ .....(2)
Adding eq (1) and eq(2), we get
⇒ 52(1/x + 1/y) = 33/2
⇒ $(\frac{1}{x}\; + \;\frac{1}{y} = \frac{{33}}{{104}})$ ......(3)
Subtracting eq (1) from eq(2), we get
⇒ 12(1/x – 1/y) = 1/2
⇒ $(\frac{1}{x}\; - \;\frac{1}{y} = \frac{1}{{24}})$ ......(4)
Adding eq (3) and eq (4), we get
⇒ 2/x = 14/39
⇒ x = 5.57 kmph
⇒ Substitute x in eq (3), we get
⇒ 1/(5.57) – 1/y = 1/24
⇒ y = 7.25 kmph
Upstreamrate is 5.57 kmph and rate downstream is 7.25 kmph
∴ Rate of current = $(\frac{{7.25\; - \;5.57}}{2})$ = 0.84 kmph