A boat travels 7.5 km upstream and 20 km downstream in 4 hours and 30 minutes. The same boat takes two hours less to travel 10 km downstream and 4.5 km upstream. Calculate the difference in speed of the boat with and against the flow?
A boat travels 7.5 km upstream and 20 km downstream in 4 hours and 30 minutes. The same boat takes two hours less to travel 10 km downstream and 4.5 km upstream. Calculate the difference in speed of the boat with and against the flow?
1). 10 km/hr
2). 2 km/hr
3). 7 km/hr
4). 6 km/hr
1 answers
Let the speed of boat in still water be x km/hr and the speed of the current be y km/hr.
Speed of boat in downstream motion = (x + y) km/hr
Speed of boat in upstream motion = (x – y) km/hr
According to the question,
$(\frac{{20}}{{x + y}} + \frac{{7.5}}{{x - y}} = 4.5)$ ----(1)
And, $(\frac{{10}}{{x + y}} + \frac{{4.5}}{{x - y}} = 2.5)$ ----(2)
On solving eq.(1) and eq.(2), we get x = 6.5 km/hr and y = 3.5 km/hr
Speed of the boat downstream = x + y = 6.5 + 3.5 = 10km/hr
Speed of the boat upstream = x – y = 6.5 – 3.5 = 3km/hr
Difference in speed = 10 – 3 = 7km/hr
∴ The difference in speed of the boat in both the motions is 7 km/hr.Other Questions
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