Question

The county's new asphalt paving machine can surface 1 km of highway in 10 h. A much older machine can surface 1 km in 18 h. How long will it take them to surface 21 km of highway if they start at opposite ends and work day and night?​

Answer 1

To calculate the time needed for two paving machines to surface 21 km of highway, combine their rates (0.1 km/h and 0.0556 km/h) to find a total rate of 0.1556 km/h, then divide the distance by the combined rate resulting in approximately 135 hours.

Step-by-step explanation:

The student's question involves calculating the time it would take for two asphalt paving machines to surface 21 km of highway, working from opposite ends. We're given that one machine can surface 1 km of highway in 10 hours, and the other in 18 hours.

To find the total time, we must determine their combined rate of work and then apply it to the total distance to be covered.

Step-by-Step Solution:

1. Calculate the rate of the new machine: 1 km / 10 hours = 0.1 km/h.
2. Calculate the rate of the older machine: 1 km / 18 hours = 0.0556 km/h.
3. Add the rates of the two machines to get the combined rate: 0.1 km/h + 0.0556 km/h = 0.1556 km/h.
4. Since the machines are working towards each other, we divide the total distance by the combined rate to find the time they will meet: 21 km / 0.1556 km/h = approximately 135 hours.

Therefore, it will take approximately 135 hours for both machines to surface the entire 21 km of highway, working from opposite ends.