One paving machine can surface 1 km of highway in 6 hours. Another can surface 1 km of highway in 8 hours. how long would it take to surface 1 km of highway with the two machines working together?
To find the time it takes for the two machines to surface 1 km of highway when working together, we can use the concept of their combined work rate.
Let's find the work rates of each machine first:
Machine 1: 1 km of highway in 6 hours
Machine 2: 1 km of highway in 8 hours
We can calculate the work rates by taking the reciprocal of the time it takes for each machine to complete 1 km of highway:
Machine 1 rate: 1 km / 6 hours = 1/6 km/hour
Machine 2 rate: 1 km / 8 hours = 1/8 km/hour
Now that we have the work rates of each machine, we can determine their combined work rate by adding their individual work rates:
Combined work rate = Machine 1 rate + Machine 2 rate = 1/6 + 1/8 km/hour
To simplify the calculation, we need to find a common denominator for the fractions:
1/6 + 1/8 = 4/24 + 3/24 = 7/24 km/hour
So, the combined work rate of the two machines working together is 7/24 km/hour.
To determine the time it would take for the two machines working together to surface 1 km of highway, we can use the formula:
Time = Distance / Rate
Time = 1 km / (7/24 km/hour)
To divide by a fraction, we multiply by the reciprocal:
Time = 1 km * (24/7 km/hour)
The km unit cancels out, leaving us with the result in hours:
Time = 24/7 hours
Therefore, it would take approximately 3.43 hours (or 3 hours and 26 minutes) for the two machines working together to surface 1 km of highway.