Question

1. writing in math a truck driver estimates that it will take him 12 hours to drive 1,160 km. after 5 hours, he has driven 484 km. is he on schedule? explain.

Explanation:

Step1: Calculate planned speed

To find the planned speed, we use the formula \( \text{speed} = \frac{\text{distance}}{\text{time}} \). The planned distance is \( 1160 \) km and planned time is \( 12 \) hours. So, planned speed \( v_{plan} = \frac{1160}{12} \approx 96.67 \) km/h.

Step2: Calculate actual speed

The actual distance driven is \( 484 \) km in \( 5 \) hours. Using the same speed formula, actual speed \( v_{actual} = \frac{484}{5} = 96.8 \) km/h.

Step3: Compare speeds

Since \( 96.8>96.67 \), the actual speed is greater than the planned speed. This means he is covering distance faster than planned, so he is on schedule (and even ahead of schedule).

Answer:

Yes, he is on schedule. The planned speed is approximately \( \frac{1160}{12}\approx96.67 \) km/h and the actual speed is \( \frac{484}{5} = 96.8 \) km/h. Since the actual speed (\( 96.8 \) km/h) is greater than the planned speed (\( \approx96.67 \) km/h), he is covering distance faster than planned, so he is on schedule.