Aboat covers 120 km downstream in 8 hours and the same distance covers in upstream in
40 hours. If the speed of boat in still water and speed of stream is increased by 6 kmph
and 4 kmph respectively, then what is the total time taken by the boat to covers 200 km in
upstream and downstream?
Answer:
Upstream = 40 hours
Downstream = 8 hours
Step-by-step explanation:
Suppose the speed of boat in still water = x.
and the speed of stream = y.
In upstream, speed = x – y.
In downstream, speed = x + y.
Time = Distance / Speed
[tex] \frac{120}{x + y} = 8 \\ \frac{15}{x + y} = 1 \\ x + y = 15 \: \: \: …(1)[/tex]
[tex] \frac{120}{x – y} = 40 \\ \frac{3}{x – y} = 1 \\ x – y = 3 \: \: \: …(2)[/tex]
Adding (1) and (2), 2x = 18 so x = 9.
And we get, y = 6.
New speed of boat = 15 kmph
New speed of stream = 10 kmph.
New upstream speed = 5 kmph.
New downstream speed = 25 kmph.
Time for upstream = Distance / Speed = 200/5 = 40 hours.
Time for downstream = Distance / Speed = 200/25 = 8 hours.
Took me long time to answer, really hope this helps.