Final answer:
To show that the difference in time taken for the two journeys is 2000÷x(x+10), we need to find the time taken for each journey. By dividing the distance traveled by the average speed, we can calculate the time taken for the first journey and the second journey. Simplifying the expression gives us the difference in time taken, which is -2000÷x(x+10). Substituting x=80, we find that the difference in time taken for the two journeys is -13.2 minutes.
Step-by-step explanation:
To show that the difference in time taken for the two journeys is 2000÷x(x+10), we need to find the time taken for each journey. The time taken for a journey can be calculated by dividing the distance traveled by the average speed. For the first journey, the distance is 200 km and the average speed is (x+10) km/h. Therefore, the time taken for the first journey is 200 / (x+10) hours. Similarly, for the second journey, the average speed would be x km/h and the time taken would be 200 / x hours.
Now, to find the difference in time taken for the two journeys, we subtract the time taken for the second journey from the time taken for the first journey:
(200 / (x+10)) - (200 / x) = [(200x - 200(x+10)) / x(x+10)]
Simplifying the expression, we get:
(200x - 200x - 2000) / x(x+10) = -2000 / x(x+10) = -2000÷x(x+10)
So, the difference in time taken for the two journeys is -2000÷x(x+10).
Now, if we substitute x=80, we can calculate the answer in minutes.
-2000÷(80)(80+10) = -2000÷(80)(90) = -2÷9 = -0.22 hours.
To convert hours to minutes, we multiply by 60:
-0.22 hours * 60 minutes/hour = -13.2 minutes.
Therefore, when x=80, the difference in time taken for the two journeys is -13.2 minutes.