A woman went for a 48km drive in her car, partly in town in the country. She drove at an average of 40km/hr in town and an average speed of 50km/hr in the country. If the drive took her one hour altogether then how long did she drive in the country?
X hrs in town.
(1-X) hrs in country.
40x + 50(1-x) = 48 km
40x + 50-50x = 48
-10x = -2
X = 0.2 Hours in town
1-X = 1-0.2 = 0.8 hrs = 48 min. in the
country.
To determine the time spent driving in the country, we can use the concept of average speed. Average speed is defined as the total distance traveled divided by the total time taken.
Let's denote the time spent driving in the country as 't' hours. Since the total drive took one hour, the time spent driving in town would be '1 - t' hours.
Using the formula for average speed, we can write:
Average speed = Total distance / Total time
For the drive in town:
40 km/hr = (distance in town) / (1 - t) hr
For the drive in the country:
50 km/hr = (distance in the country) / t hr
We are given that the total distance traveled is 48 km. Therefore, we can write:
(distance in town) + (distance in the country) = 48 km
To solve these equations, we can rearrange the first equation to find the distance in town:
(distance in town) = 40 km/hr * (1 - t) hr
Substituting this into the second equation, we have:
50 km/hr * t hr = 40 km/hr * (1 - t) hr + (distance in the country)
Simplifying further:
50t = 40 - 40t + (distance in the country)
50t + 40t = 40 + (distance in the country)
90t = 40 + (distance in the country)
As given, the total distance traveled is 48 km:
90t = 40 + 48
90t = 88
t = 88 / 90
t ≈ 0.9778
Therefore, the woman drove in the country for approximately 0.9778 hours, which is equivalent to approximately 58.67 minutes or 58 minutes and 40 seconds.