A crew team rows a boat at a rate of 20 km/h in still water. In practice on a river, the team rows for 30 minutes up the river (against the current), and then for 30 minutes down the river (with the current). The speed of the river current is 1.5 km/h. How much farther did they travel in the second 30 minutes?
2.0 km
3.0 km
1.5 km
0.75 km
half an hour up the river, 0.75 km less than still water
half an hour down the river, 0.75 more than in still water
so
0.75 + 0.75 = 1.5 km
d1 = V*T = (20-1.5) * 30/60 = 9.25 km up stream.
d2 = V*T = (20+1.5) * 30/60 = 10.75 km down stream.
d2-d1 = 10.75 - 9.25 = 1.5 km farther.
To solve this problem, we need to understand the concept of relative velocity.
The crew team's speed in still water is 20 km/h. However, when they row against the current, the speed of the river current (1.5 km/h) must be subtracted from their speed in still water. Similarly, when they row with the current, the speed of the river current must be added to their speed in still water.
Let's calculate the speeds in each scenario:
1. Rowing against the current: The crew team rows for 30 minutes, which is 30/60 = 0.5 hours. Their total speed is the sum of their speed in still water (20 km/h) and the speed of the river current (-1.5 km/h since they are going against it). So, their speed against the current is 20 - 1.5 = 18.5 km/h.
2. Rowing with the current: The crew team rows for 30 minutes, which is again 0.5 hours. Their total speed is the sum of their speed in still water (20 km/h) and the speed of the river current (1.5 km/h since they are going with it). So, their speed with the current is 20 + 1.5 = 21.5 km/h.
Now, let's calculate how far they traveled in each scenario:
1. Distance rowed against the current: Distance = Speed × Time = 18.5 km/h × 0.5 hours = 9.25 km.
2. Distance rowed with the current: Distance = Speed × Time = 21.5 km/h × 0.5 hours = 10.75 km.
To find out how much farther they traveled in the second 30 minutes, we need to subtract the distance rowed against the current from the distance rowed with the current:
10.75 km - 9.25 km = 1.5 km.
Therefore, the crew team traveled 1.5 km farther in the second 30 minutes.