Answer: (110x + 330) / [(3x + 2) * (4x + 5)] km/h
Explanation:
To determine the difference in the time it took Timmy to drive from Toronto to Barrie and back, we need to calculate the time taken for each leg of the journey separately.
Let's start with the trip from Toronto to Barrie. The distance traveled is 110 km, and the speed is 3x + 2 km/h. We can use the formula time = distance/speed to calculate the time taken for this leg of the journey:
Time taken on the trip there = Distance/Speed
= 110 km / (3x + 2) km/h
Next, calculate the time taken on the trip back from Barrie to Toronto. The distance traveled is still 110 km, but the speed is now 4x + 5 km/h. Applying the formula again:
Time taken on the trip back = Distance/Speed
= 110 km / (4x + 5) km/h
Now, we can find the difference in the time it took between driving there and driving back:
The difference in time = time taken on the trip there - Time taken on the trip back
= (110 km / (3x + 2) km/h) - (110 km / (4x + 5) km/h)
To simplify this expression further, we can find a common denominator:
Difference in time = (110 km * (4x + 5) - 110 km * (3x + 2)) / [(3x + 2) * (4x + 5)] km/h
= (440x + 550 - 330x - 220) / [(3x + 2) * (4x + 5)] km/h
= (110x + 330) / [(3x + 2) * (4x + 5)] km/h
Therefore, the simplified expression for the difference in the time it took between driving there and driving back is (110x + 330) / [(3x + 2) * (4x + 5)] km/h.