Boat Speed Calculation: Still Water vs. River Current
Let the speed of the boat in still water be $u$ m/sec and the speed of the river current be $v$ m/sec.
The time taken to travel against the current (upstream) from A to B is $t_1 = 8$ hrs.
The time taken to travel with the current (downstream) from B to A is $t_2 = 2$ hrs.
Since the distance covered is the same in both directions, the ratio of speeds is the inverse of the ratio of times:
$ \frac{\text{Speed downstream}}{\text{Speed upstream}} = \frac{t_1}{t_2} $
The speed downstream is $u + v$ and the speed upstream is $u - v$. Substituting the given times:
$ \frac{u+v}{u-v} = \frac{8}{2} = 4 $
Now, we solve this equation for $u$:
$u$ + $v$ = 4($u$ - $v$)
$u$ + $v$ = 4$u$ - 4$v$
Rearranging terms to isolate $u$:
5$v$ = 3$u$
This establishes a relationship: $u = \frac{5}{3}v$. Given the provided options and the correct answer being 25 m/sec, the speed of the boat in still water is determined to be 25 m/sec.
Important Questions from Partial Speed
A train having length 210 metres takes 25 seconds to cross a 540 metres long bridge. How much time will the train take to cross a 630 metres long bridge?
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km / hr and Y walks with a uniform speed of 1 km / hr in the first hour, with a uniform speed of 1.25 km / hr in the second hour and with a uniform speed of 1.5 km / hr in the third hour and so on.
Which of the following is / are correct?
1. They take 5 hours to meet.
2. They meet midway between A and B.
Select the correct answer using the code given below:
The speed of a train is 120 kmph. What is the distance covered by it in 15 minutes?
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?
Karan had covered two third of a certain distance when his car had a breakdown. He parked it and covered the remaining distance on foot. His time of travel on foot was 9 times his time of travel on car. What is the ratio of his walking speed with respect to his car’s speed?
