To find the speed you need to travel for the rest of the way in order to have an average speed of 60 km/h over the entire trip, we can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the total time for the trip:
The distance to the town is 60 km, and you traveled halfway at a speed of 30 km/h. So the time taken for the first half of the trip is:
Time taken for the first half = Distance / Speed = 60 km / 30 km/hr = 2 hours
Now, we can calculate the total time for the entire trip:
Total Time = Time taken for the first half + Time taken for the second half
Since you traveled halfway to the town at a speed of 30 km/hr, the remaining distance is also 60 km.
So, for the second half of the trip, we have:
Time taken for the second half = Distance / Speed
To obtain an average speed of 60 km/hr over the entire trip, we can set up the equation:
60 km/hr = (60 km + 60 km) / (2 hours + Time taken for the second half)
Simplifying this equation, we get:
60 km/hr = 120 km / (2 + Time taken for the second half)
Cross-multiplying, we have:
60 km/hr * (2 + Time taken for the second half) = 120 km
Simplifying further, we get:
120 + 60 * Time taken for the second half = 120 km
60 * Time taken for the second half = 0 km
From this equation, we can see that the time taken for the second half of the trip is 0 hours. This means that the remaining distance of 60 km cannot be covered in any amount of time. Therefore, it is not possible to have an average speed of 60 km/hr over the entire trip.
Hence, the correct answer is D) None of these.