the countrys new asphalt paving machine can surface 1 km of

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

Solution

the new machine can surface the road at a rate of 1/10 km per hour
the old machine can surface the road at a rate of 1/18 km per hour
working together, the two machines can surface a road at the rate of (1/10 + 1/18) km per hour.
That comes to: 7/45 km per hour
Another way of saying the above is,
the two machines can cover 7/45 km per hour or
it takes them 45/7 hrs to cover 1 km
So it will take them,
21x(45/7) hrs to cover 21 km
21x(45/7) = 3x45 = 135 hrs
Ans: 135 hrs