Correct option is D
Given:
The ratio of the speed of the motorboat (in still water) to the speed of the current is 31:6.
Time taken to travel downstream = 4 hours 10 minutes =
46010hours=60250hours=625hours.
Concept Used:
Downstream speed is the speed of the boat plus the speed of the current.
Upstream speed is the speed of the boat minus the speed of the current.
Distance covered downstream = Distance covered upstream (since the motorboat returns to its starting point).
Formula Used:
Downstream Speed:
downstream=vboat+vcurrent
Upstream Speed:
upstream=vboat−vcurrent
Distance Formula:
Distance=Speed×Time
Solution:
Let the speed of the boat in still water be 31x km/h and the speed of the current be 6x km/h.
Downstream speed:
vdownstream=31x+6x=37x km/h
Upstream speed:
vupstream=31x−6x=25x km/h
Distance covered downstream:
Distance=vdownstream×Time downstream=37x×625 km
Time taken to cover the same distance upstream:
Let the time taken upstream be
tupstream.
Distance=vupstream×tupstream=25x×tupstream km
Since the distance covered is the same in both directions:
x×625=25x×tupstream
Solving for
tupstream:
tupstream=25x37x×625=2537×625=637 hours
Therefore; The time taken by the motorboat to come back to its initial point (upstream) is
637hour
s or
6 hours 10 minutes.
Alternate Method:
English
80 Questions
160 Marks
60 Mins
