A river flows at 3km/h. At what speed must a boat travel in order to make a 35km trip upstream in a time of 50 minutes?
How long will it take the boat to make the return trip downstream? (Assume the boat retains the speed travelled upstream)
Working out please
BAD QUESTION
To find the speed the boat must travel to make a 35km trip upstream in a time of 50 minutes, we need to consider the velocity of the river and the relative motion of the boat.
Let's assume the speed of the boat is B km/h.
Upstream velocity = Speed of the boat - Velocity of the river
Downstream velocity = Speed of the boat + Velocity of the river
Given that the river flows at 3 km/h, the upstream velocity is B - 3 km/h.
We can use the formula:
Time = Distance / Speed
To solve the first part of the problem, we have:
50 minutes = 35 km / (B - 3 km/h)
To find the speed of the boat, we can rearrange the equation:
50 minutes * (B - 3 km/h) = 35 km
(B - 3 km/h) = 35 km / 50 minutes
B - 3 km/h = 0.7 km/h
Adding 3 km/h to both sides:
B = 3.7 km/h
So, the boat must travel at a speed of 3.7 km/h to make the 35 km trip upstream in a time of 50 minutes.
For the second part of the problem, we know that the downstream velocity is B + 3 km/h.
The time it takes for the boat to make the return trip downstream can be calculated using the same formula:
Time = Distance / Speed
Let's assume the distance is still 35 km. Therefore:
Time = 35 km / (B + 3 km/h)
Substituting B = 3.7 km/h:
Time = 35 km / (3.7 km/h + 3 km/h)
Time = 35 km / 6.7 km/h
Time ≈ 5.22 hours
So, it will take the boat approximately 5.22 hours to make the return trip downstream.
To determine the speed the boat must travel upstream to make a 35km trip in 50 minutes, we need to take into account the speed of the river.
Let's denote the speed of the boat as 'b' km/h. Since the boat is traveling upstream, it will be moving against the current of the river. Hence, the effective speed will be the difference between the boat's speed and the speed of the river.
The formula to calculate the effective speed when moving against the current is:
Effective speed = Boat's speed - River's speed
Given that the river flows at 3 km/h, the effective speed upstream will be:
Effective speed = b km/h - 3 km/h
Now, let's convert the time given (50 minutes) to hours:
50 minutes = 50/60 = 5/6 hours
To find the time taken for the upstream trip, we can use the formula:
Time = Distance / Speed
Substituting the given values:
5/6 hours = 35 km / (b km/h - 3 km/h)
To solve for 'b', we can cross-multiply and solve the resulting equation:
(5/6) * (b km/h - 3 km/h) = 35 km
Multiplying both sides by 6/5:
b km/h - 3 km/h = 35 km * (6/5)
Simplifying the equation:
b - 3 = 42
Adding 3 to both sides, we get:
b = 45 km/h
Therefore, the boat must travel at a speed of 45 km/h upstream to make the 35 km trip in 50 minutes.
Now, to calculate the time it would take the boat to make the return trip downstream, we can use the same effective speed, as the boat retains its speed when traveling downstream.
The distance for the return trip is still 35 km. Using the formula:
Time = Distance / Speed
Time = 35 km / (45 km/h - 3 km/h)
Time = 35 km / 42 km/h
Simplifying:
Time = 5/6 hours
Converting to minutes:
Time = (5/6) * 60 = 50 minutes
So, it will also take the boat 50 minutes to make the return trip downstream, assuming it retains the speed it traveled upstream.
u = boat speed
u-3 = upstream speed
u+3 = downstream speed
distance = speed * time
35 = (u-3) * 5/6
210 = 5u - 15
225 = 5u
45 = u
downstream,
35 = 48 * t
t = 35/48
t = 0.729 hr = 43min 45 sec