A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is :
0.5 km/hr
1 km/hr
3.5 km/hr
1.8 km/hr
Explanation:
Suppose he move 4 km downstream in x hours. Then,
Speed downstream =($\dfrac{4}{x}$) km/hr
Speed upstream =( $\dfrac{3}{x}$ ) km/hr
∴ $\dfrac{48}{(4/x)} $+ $\dfrac {48} {(3/x)} $ =14 or x= $\dfrac{1}{2}$
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2(8−6)km/hr=1km/hr
Suppose he move 4 km downstream in x hours. Then,
Speed downstream =($\dfrac{4}{x}$) km/hr
Speed upstream =( $\dfrac{3}{x}$ ) km/hr
∴ $\dfrac{48}{(4/x)} $+ $\dfrac {48} {(3/x)} $ =14 or x= $\dfrac{1}{2}$
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2(8−6)km/hr=1km/hr