Can someone explain this for me step by step? Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.

Question

anonymous · Answer

am i using r=d/t

hero · Answer

use d = rt and let r = b ± w

anonymous · Answer

ok

anonymous · Answer

what does let r = b ± w mean

hero · Answer

t1 = Upstream time
t2 = Downsteam time

10 = 5t
2 = t1

t1 + t2 = 3
2 + t2 = 3
t2 = 3 - 2
t2 = 1

I'll show you what that means in a sec

anonymous · Answer

ok thank you

hero · Answer

Upstream Formula
d = rt1
d = (b - w)t1

Downsteam Formula:
d = rt2
d = (b + w)t2

hero · Answer

b - w = 5

hero · Answer

Upstream
10 = 2(b - w)

Downsteam
10 = (b + w)

10 = 2b - 2w
20 = 2b +2w

30 = 4b
30/4 = b
7.5 = b

hero · Answer

10 = b + w
10 = 7.5 + w
10 - 7.5 = w
2.5 = w

hero · Answer

Therefore
The speed of the boat was 7.5 km/h

hero · Answer

Any questions?

anonymous · Answer

do you have to do both equations

hero · Answer

You don't have to solve for w in this case, however, it is good to practice doing so.

anonymous · Answer

ok that makes it easier to follow

anonymous · Answer

so if I put both equations then I would be correct as well

anonymous · Answer

what does the b and w stand for if you dont mind

anonymous · Answer

hello

anonymous · Answer

so confused

hero · Answer

b = speed of the boat
w = speed of the water current

hero · Answer

@andjie

anonymous · Answer

Thank you

hero · Answer

All you have to do is just keep doing similar problems like these. You'll get the hang of it.

anonymous · Answer

thank you so much, sorry I left