Final answer:
To find the number of kilometers of good surface, we set up an equation with the distances and speeds provided. Solving the equation reveals that there are 36 kilometers of good surface and 12 kilometers of bad surface on the 48 km trip.
Step-by-step explanation:
To solve the problem of a man driving a distance of 48 km in 45 minutes with different speeds on varying road conditions, we need to set up an algebraic equation. Let's denote the number of kilometers of good surface as x and the number of kilometers of bad surface as (48 - x).
Since we know the speed on the good surface is 72 km/hr and on the bad surface is 48 km/hr, we can calculate the time taken for each part of the journey:
- Time on good surface = distance/speed = x/72 hours
- Time on bad surface = distance/speed = (48 - x)/48 hours
The total time for the trip is 45 minutes, which is 0.75 hours (since 45 minutes is 3/4 of an hour). Setting up the equation with the total time:
x/72 + (48 - x)/48 = 0.75
To solve this equation, we find a common denominator, which is 144, and rewrite the equation:
2x + 3(48 - x) = 108
Simplify and solve:
2x + 144 - 3x = 108, which gives -x = -36, hence x = 36 km.
Therefore, there are 36 kilometers of good surface and 12 kilometers of bad surface.