A man rows to a place 24 km distance and come back in 7 hours.
A man rows to a place 24 km distance and come back in 7 hours. He finds that he can row 2 km with the up stream in the same time as 3 km against the down stream. The rate of the stream is
Answer/Solution
20/7 km/hr
Steps/Work
Explanation:
Speed down stream = distance/time = 3/x
Speed up stream = distance/time = 2/x
Time taken to row 24 km up stream and down stream is
= 48/(2/x) + 48/(3/x)
= 48x/2 + 48x/3 = 48x(5/6) = 8x+5 = 40x
40x = 7
x = 7/40 hr
Speed of down stream 3/(7/40) = 120/7
speed of up stream = 2/(7/40) = 80/7
Rate of stream = 1/2(a - b) = 1/2[(120/7)-(80/7)]
= 1/2(40/7)
= 20/7 km/hr
Answer: Option C
Speed down stream = distance/time = 3/x
Speed up stream = distance/time = 2/x
Time taken to row 24 km up stream and down stream is
= 48/(2/x) + 48/(3/x)
= 48x/2 + 48x/3 = 48x(5/6) = 8x+5 = 40x
40x = 7
x = 7/40 hr
Speed of down stream 3/(7/40) = 120/7
speed of up stream = 2/(7/40) = 80/7
Rate of stream = 1/2(a - b) = 1/2[(120/7)-(80/7)]
= 1/2(40/7)
= 20/7 km/hr
Answer: Option C