Question

Chan rows at a rate of eight miles per hour in still water. On Wednesday, it takes him three hours to row upstream from his house to the park. He rows back home, and it takes him two hours. What is the speed of the current?

Answer 1

What is the choice?

Answer 2

The rate of Chan’s rowing in still water is 8 mph.
Chan rows from the house to the park on Wednesday.
Chan’s house is next to a river.
The entire trip takes five hours.

Answer 3

distance = speed * time (I'll use d = st for short)

the distance between the park and his house is the same both ways. so we can write a distance equation for each trip and set them equal to each other.

we also need to take into account the speed of the current. we can let c = speed of current.

when he goes along with the current, the current helps him go faster. therefore, his speed with the current = s + c

when he goes against the current, he's slower since he's fighting the current. therefore, his speed against the current is s - c

Answer 4

so, writing the equations:

\[s_{park}*t_{park} = s_{home}*t_{home} \]

where s_park is the speed going to the park
t_park is the time taken to go to the park
s_home is the speed taken to get home
t_home is the time taken to get to the home

and filling in information from the problem:
- "chan rows at a rate of 8 miles per hour in still water" so s_park and s_home both start at 8.
- "it takes him 3 hours to row upstream from his house to the park" so t_park = 3
- "he rows back home and it takes 2 hours" so t_home = 2

Answer 5

plugging things in:

(8-c)(3) = (8+c)(2)

solve for c.

let me know you need me to explain anything in more detail, or you just want to check your work