In your job as a secret agent, you are given the mysterious instruction to take
ID: 1777940 • Letter: I
Question
In your job as a secret agent, you are given the mysterious instruction to take a Zodiac boat (Links to an external site.)Links to an external site. out on a river and drop a secret listening device into the river.
Update: the device drifts with the flow of the river.
You are then to take the boat at top speed upstream for 10 minutes, then turn around and head back at top speed to retrieve the device. On the upstream leg you travel 9 km, and on the way back you travel 11 km. How long does the return take? How fast is the river flowing? What is the boat speed relative to the water?
Explanation / Answer
let maximum speed of the boad relative to still water be u
let speed of river stream be v
so speed relative to ground while travelling upstreram = u - v
distnace, d1 = 9000 m
time t1 = d1/(u - v) = 9000/(u - v)
speed of boat wrt ground while coming downstream = v + u
distnace d2 = 11,000 m
time t2 = 11,000/(v + u)
now, in thhe time t1 + t2 the device has moved distance 2 km with speed v
v = 2000/(t1 + t2)
also, t1 = 10 min = 600 sec
600 = 9000/(u - v)
u - v = 15
v = 2000/(600 + t2) = 2000(v + u)/(600(v + u) + 11000)
600v^2 + 600uv + 11000v = 2000v + 2000u
600v^2 + 600(15 + v)v + 9000v - 2000(15 + v) = 0
1200v^2 + 7000v + 9000 - 30,000 = 0
1200v^2 + 7000v - 21000 =0
1.2v^2 + 7v - 21 = 0
solving for v
speed of river v = 2.183 m/s
speed of boat, u = 17.183 m/s
hence return time, t2 = 11,000/(19.183) = 573.423 s = 9.557 s