My greatest mistake this week was with a word question involving finding the speed of a boat
the question was:
To prevent grounding, a cruise ship anchors 18 km away from a river port. To transport the passengers to the port, the crew uses smaller boats. The smaller boats travel 12 km downstream in the same time it takes them to travel 8 km upstream.
a) If the speed of the current is 6 km/hr, write expressions for the speed of the boat travelling upstream and travelling downstream.
b) Calculate the time it takes for the small boats to travel upstream from the cruise ship to the port.
I got the correct for answer for part a:
Since you need to find the speed traveling both upstream and downstream you need to have 2 equations.
To do this first you can make a variable for speed in still water which here will be x.
Since we know the current is moving 6km/h, the speeds for moving upstream and downstream is just the speed in still plus the current
So moving downstream the speed is: x = x + 6
for upstream the speed is: x = x -6
The part is made is a mistake with is in part b
Since we know the speed for going upstream is the same as going downstream, I wrote the equation:
However this is incorrect and lead me to the wrong answer. What I should have done is make the 2 expressions equal to each other. Since the expressions are the both the equation for time (distance/speed), writing them equal to each other is saying they both are the same time:
From here you can cross multiply. Multiply the 8 by x + 6, and multiply 12 by x – 6.
and from their you just isolate and solve for x which gets you your speed
After isolating X you get 4x = 120
which translates to x = 30
The the answer to part b is 30 minutes