Car travels a distance of 140 km at 70.0 km/hr. It then travels an additional distance of 60.0 km at 40.0 km/hr. The average speed is Multiple Choice ? ( 610 km/hc. ? 571 km/hr. ? 53.3 km/hr ? 467 kr. ? 45.0 km/h.
The Correct Answer and Explanation is :
To determine the average speed for the entire trip, we need to use the formula for average speed:
[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
]
Step 1: Find the total distance
The car travels two segments:
- 140 km at 70.0 km/h
- 60.0 km at 40.0 km/h
Total Distance = 140 km + 60.0 km = 200 km
Step 2: Calculate the time for each segment
Now we calculate the time taken for each segment using the formula:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
]
- Time for the first segment:
[
\text{Time}_1 = \frac{140 \, \text{km}}{70.0 \, \text{km/h}} = 2 \, \text{hours}
]
- Time for the second segment:
[
\text{Time}_2 = \frac{60.0 \, \text{km}}{40.0 \, \text{km/h}} = 1.5 \, \text{hours}
]
Step 3: Find the total time
Total Time = Time for the first segment + Time for the second segment
Total Time = 2 hours + 1.5 hours = 3.5 hours
Step 4: Calculate the average speed
Now we can calculate the average speed:
[
\text{Average Speed} = \frac{200 \, \text{km}}{3.5 \, \text{hours}} = 57.14 \, \text{km/h}
]
Step 5: Round the answer
Rounding the result to the nearest value from the options, we get approximately 57.1 km/h, which is closest to 57.3 km/h in the options provided.
Thus, the correct average speed is 57.1 km/h (which is not explicitly listed but closest to 53.3 km/h based on rounding conventions).