Jack, jill and spot go out for a picnic at the side of the river. jack takes spot for a jog. jack and spot are on the wast bank of the 30m wide river when jill is on the east side. the rivers current is 0.75m/s south.

a) spot jumps into the river and swims straight east at 1.8m/s relitive to the water. once across spot runs 4m/s on the shore to get to jill. How long does to take spot to get to jill?
b)jack dives in the river and aims slightly upstream and swims 2m/s relitive to the water to go straight across. How many seconds does jack beat spot by?

see other post.

a) To find out how long it takes for Spot to get to Jill, we need to calculate the time it takes for Spot to cross the river and the time it takes to run along the shore.

1. Time to cross the river: We can calculate the distance Spot travels across the river by multiplying his speed relative to the water (1.8 m/s) by the width of the river (30 m). This gives us a distance of 54 meters. Now, to find the time, we divide the distance by Spot's speed relative to the water. So, 54 m / 1.8 m/s = 30 seconds.

2. Time to run along the shore: Spot runs at a speed of 4 m/s. Since we know the distance between Spot and Jill is the width of the river, which is 30 meters, we divide this distance by Spot's running speed to find the time. So, 30 m / 4 m/s = 7.5 seconds.

Finally, to find the total time it takes for Spot to get to Jill, we add the time to cross the river (30 seconds) and the time to run along the shore (7.5 seconds):
Total time = 30 seconds + 7.5 seconds = 37.5 seconds.

Therefore, it takes Spot 37.5 seconds to get to Jill.

b) To determine how many seconds Jack beats Spot by, we need to calculate the time it takes for Jack to cross the river and compare it to the time it takes for Spot.

1. Time for Jack to cross the river: Jack swims 2 m/s relative to the water. Since the river's current is 0.75 m/s south, Jack needs to swim upstream, and his effective speed is reduced by the river's current. So, Jack's effective speed is 2 m/s - 0.75 m/s = 1.25 m/s. To calculate the time it takes for Jack to cross the river, we divide the width of the river (30 m) by Jack's effective speed: 30 m / 1.25 m/s = 24 seconds.

2. Time for Spot to get to Jill: We already calculated in part (a) that Spot takes 37.5 seconds to reach Jill.

To find the time difference, we subtract the time it takes for Spot to get to Jill from the time it takes for Jack: 37.5 seconds - 24 seconds = 13.5 seconds.

Therefore, Jack beats Spot by 13.5 seconds.