A motorboat can travel upstream on a river at 18km/h and downstream at 30km/h. How far upsteam can the boat travel if it leaves at 8am and must return by noon?
To calculate how far upstream the boat can travel, we need to consider the time available and the speeds of the boat.
Given:
- Upstream speed: 18 km/h
- Downstream speed: 30 km/h
To determine the distance traveled upstream, we need to know the time it takes to travel upstream and downstream. Since the boat must return by noon, the available time is 4 hours (from 8am to 12pm).
Let's break down the problem into steps:
Step 1: Calculate the time taken to travel downstream
To determine the time taken to travel downstream, we divide the distance by the downstream speed.
Time downstream = Distance / Downstream speed
Step 2: Calculate the time taken to travel upstream
Similarly, to determine the time taken to travel upstream, we divide the distance by the upstream speed.
Time upstream = Distance / Upstream speed
Step 3: Calculate the total time taken for the round trip
Since the boat must return by noon, the round trip time is 4 hours.
Step 4: Set up the equation
Total time taken = Time downstream + Time upstream
Step 5: Solve for the distance
Now we can solve for the distance traveled upstream by rearranging the equation:
Distance = (Total time taken - Time downstream) * Upstream speed
Let's substitute the given values and calculate the distance:
Time downstream = Distance / Downstream speed = Distance / 30 km/h
Time upstream = Distance / Upstream speed = Distance / 18 km/h
Total time taken = 4 hours
Distance = (Total time taken - Time downstream) * Upstream speed
= (4 hours - (Distance / 30 km/h)) * 18 km/h
Solve for distance:
Distance = (4 - (Distance / 30)) * 18
Simplifying the equation:
Distance = 72 - (1.2 * Distance / 30)
Distance = 72 - 0.04 * Distance
Bringing all the terms to one side:
1.04 * Distance = 72
Distance = 72 / 1.04
Distance ≈ 69.23 km
Therefore, the boat can travel approximately 69.23 km upstream before it needs to turn around and return by noon.