A child, who is 45 m from the bank of a river is being carried downstream by the river's swift current of 1.0 m/s. As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line until she reaches the child at a point downstream. If the lifeguard can swim 2.0 m/s relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child?

relative distance lifeguard has to swim:45 meters, swimming at 2m/s

time=45/2=22.5 seconds.

how far downstream: 1m/s*22.5s=22.5m

thanks!

bob pursley, can you answer my question. SCIENCE BIOLOGY. My name is Julia. THanks. I have till 12 am. HELPPPP

Thanks!

what rubbish

To find the time it takes for the lifeguard to reach the child, we need to calculate the time it takes for the child to reach the intercept point.

Let's consider the distance the child covers until the lifeguard reaches the intercept point. This distance comprises two components:

1. The distance covered downstream by the child due to the river's current.
2. The distance covered downstream by the lifeguard to intercept the child.

Let's calculate each of these distances:

1. Distance covered by the child downstream:
Given that the child is being carried downstream by the river's swift current of 1.0 m/s, and considering that the time it takes for the lifeguard to reach the intercept point is the same as the child, we can use the formula: distance = rate × time.

distance_child = rate_child × time_child
distance_child = 1.0 m/s × time_child

2. Distance covered by the lifeguard downstream:
Given that the lifeguard can swim with a speed of 2.0 m/s relative to the water, the distance covered by the lifeguard downstream is:

distance_lifeguard = rate_lifeguard × time_lifeguard
distance_lifeguard = 2.0 m/s × time_lifeguard

Now, let's equate the two distances:
distance_child = distance_lifeguard
1.0 m/s × time_child = 2.0 m/s × time_lifeguard

Since the distance covered by the child is equal to the distance covered by the lifeguard when they both meet at the intercept point, we can write:
45 m = 2.0 m/s × time_lifeguard

Now we can solve for time_lifeguard:
time_lifeguard = 45 m / 2.0 m/s
time_lifeguard ≈ 22.5 seconds

So, it takes the lifeguard approximately 22.5 seconds to reach the child.

To find the distance downstream where the lifeguard intercepts the child, we can substitute the value of time_lifeguard in either of the two distance formulas:

distance_lifeguard = rate_lifeguard × time_lifeguard
distance_lifeguard = 2.0 m/s × 22.5 seconds
distance_lifeguard ≈ 45 meters

Therefore, the lifeguard intercepts the child approximately 45 meters downstream from the lifeguard's starting position.