A raft was sent away from point A downstream. A patrol-boat left A 5 hour and 20 min later and caught up with the raft 20 km away from point A. What was the speed of the raft if the speed of the patrol-boat was 12 km/hour?
Hi Anish Panda,
The answer is correct, it's just that you had to round it to 3 km per hour. It would look weird if the answer was 2.86 km.
I checked that answer, Reiny, and it wasn't right
Reiny, your answer is wrong because in your final answer you have the speed of the raft AND the speed of the current. You forgot to find the current speed.
To find the speed of the raft, we can set up a simple equation using the distance and time information given.
Let's assume the speed of the raft is "r" km/hour. Since the patrol-boat caught up with the raft 20 km away from point A, and the patrol-boat's speed is 12 km/hour, the time taken for the patrol-boat to catch up with the raft can be calculated using the formula: time = distance / speed.
For the patrol-boat, the time taken is 20 km / 12 km/hour = 5/3 hours.
Since the patrol-boat left A 5 hours and 20 minutes later, we need to convert 5 hours and 20 minutes to hours. 20 minutes is 1/3 of an hour (since there are 60 minutes in an hour), so the total time is 5 hours + 1/3 hours = 16/3 hours.
Now, we can set up an equation using the times for the patrol-boat and the raft:
time taken by patrol-boat = time taken by raft + delay
5/3 hours = (16/3 hours) + 5 hours and 20 minutes
To solve for the time taken by the raft, we can subtract the delay (which is 16/3 hours) from both sides of the equation:
5/3 hours - 16/3 hours = 5 hours and 20 minutes
Thus, the time taken by the raft is -11/3 hours, which is not possible. This means there is no reasonable solution to this question.
speed of raft ---- x km/h
speed of boat ----12 km/h
when the boat caught up with the raft, they both had gone 20 km
time for raft = 20/x
time for boat = 20/12
20/x - 20/12 = 5 hrs, 20 min = 16/3
times 12x
240 - 20x = 64x
240 = 84x
x = 240/84 km/h = 20/7 km/h
check"
time for raft = 20/(20/7) = 7 hrs
time for boat = 20/12 = 5/3 hrs
difference in time = 7 - 5/3 = 5 1/3 hours
or 5 hours and 20 minutes