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Mechanics (Maths/Physics) Help

Does anyone know how to solve this question?

A motorboat goes upstream on a river and covers the distance between two towns on the riverbank in 6 hours. It covers this distance downstream in 5 hours. If the speed of the stream is 1.5 km/h, find the speed of the boat in still water.

I'm not necessarily looking for the answer, more on how to work it out. Thank you!!

Reply 1

ghostwalker

Original post by HiImSharon

Start by letting the speed in still water by x km/h.

Then use distance = speed times time, once for going upstream, and once for coming down. Since they went the same distance in each case, we can equate the two and solve for x.

Going upstream speed will be x- 1.5

Etc.

Reply 2

HiImSharon

Original post by ghostwalker

Just wanted to double check, the distance is the speed of the stream x time?

Reply 3

ghostwalker

Original post by HiImSharon

Just wanted to double check, the distance is the speed of the stream x time?

Not quite.

You know the time of the boat's journey. So, the distance is the speed of the boat (relative to the land) times time. Hence the x-1.5 when going upstream.

Reply 4

HiImSharon

Original post by ghostwalker

Not quite.

You know the time of the boat's journey. So, the distance is the speed of the boat (relative to the land) times time. Hence the x-1.5 when going upstream.

Ah now I'm a bit confused :colondollar:

,
so for upstream the equation would be (x - 1.5) x 6?
But how do you work out the speed of the boat relative to land?

Reply 5

ghostwalker

Original post by HiImSharon

Ah now I'm a bit confused :colondollar:

,
so for upstream the equation would be (x - 1.5) x 6?
But how do you work out the speed of the boat relative to land?

You just did. The speed of the boat (in still water) is x. When it's going upstream, the water is going 1.5 km/h in the opposite direction so the speed of the boat (relative to land) is x-1.5

Reply 6

HiImSharon

Original post by ghostwalker

You just did. The speed of the boat (in still water) is x. When it's going upstream, the water is going 1.5 km/h in the opposite direction so the speed of the boat (relative to land) is x-1.5

Forgive me for being really slow, so its just a matter of solving 6(x-1.5) =5x?

Reply 7

ghostwalker

Original post by HiImSharon

Forgive me for being really slow, so its just a matter of solving 6(x-1.5) =5x?

Close, but not quite.

When the boat is coming downstream, yes, it takes 5 hours.

But it's speed is not just x. It's now moving with the current, so the speed is...?

Reply 8

ghostwalker

Original post by Zacken

Seems fine to me.

Too much?

(edited 8 years ago)

Reply 9

Zacken

Original post by ghostwalker

Too much?

Right - ignore me, I need to read the question properly. :tongue:

Reply 10

ghostwalker

Original post by Zacken

...

Sorry - couldn't resist.

Reply 11

HiImSharon

Original post by ghostwalker

Close, but not quite.

When the boat is coming downstream, yes, it takes 5 hours.

But it's speed is not just x. It's now moving with the current, so the speed is...?