The speed of a boat in still water is 18 km/h and the speed of the current is 6 km/h. In how much time (in hours) will the boat travel a distance of 90 km up stream and the same distance downstream ?

Options

A. `9 1/2`
B. `11 1/4`
C. `12`
D. `10`

Answer

To solve the problem step by step, we will calculate the time taken by the boat to travel upstream and downstream separately, and then sum them up.

### Step 1: Determine the speed of the boat upstream and downstream.
- **Speed of the boat in still water** = 18 km/h
- **Speed of the current** = 6 km/h

**Upstream speed** = Speed of the boat - Speed of the current
= 18 km/h - 6 km/h
= 12 km/h

**Downstream speed** = Speed of the boat + Speed of the current
= 18 km/h + 6 km/h
= 24 km/h

### Step 2: Calculate the time taken to travel 90 km upstream.
Using the formula:
**Time = Distance / Speed**

**Time taken upstream** = Distance / Upstream speed
= 90 km / 12 km/h
= 7.5 hours

### Step 3: Calculate the time taken to travel 90 km downstream.
Using the same formula:

**Time taken downstream** = Distance / Downstream speed
= 90 km / 24 km/h
= 3.75 hours

### Step 4: Calculate the total time taken for the round trip.
Total time = Time taken upstream + Time taken downstream
= 7.5 hours + 3.75 hours
= 11.25 hours

### Final Answer:
The total time taken to travel 90 km upstream and the same distance downstream is **11.25 hours**.

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