Final answer:
The student wants to know how much more time was spent in a boat than in a car on a 12-hour family trip. Calculation reveals that 1.92 hours more were spent in the boat than in the car.
Step-by-step explanation:
The question asks to calculate the difference in time spent traveling by car and by boat during a family vacation trip. The total trip time is 12 hours, with 4/5 in a car and 1/5 in a boat. The car travels 5 times as fast as the boat.
Let's denote the speed of the boat as 'b'. Then, the speed of the car would be '5b'. Given that 1/5 of the trip was in the boat and 4/5 in the car, we can set up ratios to find the times spent in each mode of transport.
Let 'T' be the total trip time. The distance covered by the boat and the car is the same, as they cover different fractions of the trip at different speeds. Let 'D' represent this common distance. Therefore:
- Time in boat = D/b
- Time in car = D/(5b)
As the trip ratios are 1/5 for the boat and 4/5 for the car, we can say:
- D/b = T/5
- D/(5b) = (4T/5)/5
Now, to find the difference in time spent, we subtract the time in the car from the time in the boat:
- Time difference = (D/b) - (D/(5b))
- Time difference = (T/5) - (T/25)
- Time difference = 4T/25
Since T is 12 hours:
- Time difference = (4 \times 12) / 25
- Time difference = 48/25
- Time difference = 1.92 hours
The time spent in the boat is 1.92 hours more than the time spent in the car.