During the first `18 min` of a `60 min` trip, a car has an average speed of `11 ms^-1.` What should be the average speed for remaining `42 min` so that car is having an average speed of `21 ms^-1` for the entire trip?

Options

A. `25.3 ms^(-1)`
B. `29.2 ms^(-1)`
C. `31 ms^(-1)`
D. `35.6 ms^(-1)`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert Time from Minutes to Seconds
The total trip time is given as 60 minutes, and the first segment of the trip is 18 minutes. We need to convert these times into seconds for our calculations.

- Total time of the trip = 60 minutes = \(60 \times 60 = 3600\) seconds
- Time for the first segment = 18 minutes = \(18 \times 60 = 1080\) seconds
- Time for the remaining segment = 42 minutes = \(42 \times 60 = 2520\) seconds

### Step 2: Calculate Distance for the First Segment
Using the average speed formula, we can calculate the distance traveled during the first segment of the trip.

- Average speed from A to C = 11 m/s
- Distance from A to C = Speed × Time = \(11 \, \text{m/s} \times 1080 \, \text{s} = 11880 \, \text{m}\)

### Step 3: Set Up the Equation for Total Distance
The total distance for the entire trip can also be expressed in terms of the average speed for the entire trip.

- Average speed for the entire trip = 21 m/s
- Total distance for the entire trip = Average speed × Total time = \(21 \, \text{m/s} \times 3600 \, \text{s} = 75600 \, \text{m}\)

### Step 4: Calculate Distance for the Remaining Segment
Let \(V\) be the average speed from C to B. The distance from C to B can be expressed as:

- Distance from C to B = Speed × Time = \(V \times 2520 \, \text{s}\)

### Step 5: Write the Total Distance Equation
The total distance traveled during the entire trip is the sum of the distances from A to C and C to B:

\[ 11880 \, \text{m} + V \times 2520 \, \text{s} = 75600 \, \text{m} \]

### Step 6: Solve for \(V\)
Rearranging the equation to solve for \(V\):

\[ V \times 2520 = 75600 - 11880 \]
\[ V \times 2520 = 63720 \]
\[ V = \frac{63720}{2520} \]
\[ V = 25.3 \, \text{m/s} \]

### Final Answer
The average speed for the remaining 42 minutes should be **25.3 m/s**.

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