A motorboat can travel upsteam on a river at 18km/h and downsteam at 30km/h. How far upstream can the boat travel if it leaves at 8:00am and must return by noon?
18t=30•(4-t)
18t =120 -30t
48t=120
t=120/48 =2.5
18•2.5=45 km
Thanks
To determine how far upstream the motorboat can travel and return by noon, we need to consider the speed of the boat and the time available for the round trip.
Let's break down the problem into steps:
Step 1: Determine the time available for the round trip.
A round trip requires the boat to travel upstream and then return downstream. The boat needs to return by noon, which means there are 4 hours available for the round trip (from 8:00 am to 12:00 pm).
Step 2: Calculate the time required for the upstream journey.
To calculate the time required for the upstream journey, we need to know the speed of the boat while traveling upstream. The boat's speed upstream is given as 18 km/h.
Since speed = distance/time, we can rearrange the equation to solve for time:
time = distance/speed.
Let's assume the boat can travel upstream for a certain distance, which we'll denote as "d" km. The time required for the upstream journey would then be:
time upstream = d/18 km/h.
Step 3: Calculate the time required for the downstream journey.
The boat's speed downstream is given as 30 km/h. Using the same formula, we can calculate the time required for the downstream journey:
time downstream = d/30 km/h.
Step 4: Calculate the total round-trip time.
Since the boat needs to return by noon, the total round-trip time must be less than or equal to 4 hours. Taking into account both the upstream and downstream time, we can write the following equation:
time upstream + time downstream ≤ 4.
Substituting the time formulas from steps 2 and 3:
d/18 + d/30 ≤ 4.
Step 5: Solve the inequality for d.
To solve the inequality, we need to find the maximum value of d that satisfies it.
Multiplying all terms by the least common denominator (18 * 30 = 540), we get:
30d + 18d ≤ 4 * 540,
48d ≤ 2160,
d ≤ 45.
Therefore, the boat can travel upstream for a maximum distance of 45 km and still return by noon.