Mathmatical puzzler...know the answer, but how to get the answer?

Question

A boat that will travel at the rate of 15 kph in still water. It can go upstream for 35 km in the same time it takes to go 140 km downstream. How fast is the boat traveling when it goes downstream?

The answer is 24 kph, but how do I get that? This isn't your average d=rt problem, so I'm having a little trouble...

Answer 1

The speed that the boat is traveling has to take into account the current speed (C).

So when going upstream it goes (15-C)kph, and when it goes downstream, it goes (15+C)kph.

But we also know that 4(15-C) = 15+C, since the boat goes four times as far downstream than upstream.

60 - 4C = 15 + C or 45 = 5C so the current is 9kph.

The boat goes 24kph downstream to 140km in 5.83 hours.
The boat goes 6 kph upstream to 35km in 5.83 hours.

Sometimes the simplest solution is the best. :o)

Answer 2

d=rt, so t=d/r. Let x be the change in rate of the boat when its going upstream or downstream. since we know that the boat can go upstream for 35 km in the same time it takes to go 140 km downstream we can set an equality using t=d/r. So, since time is the same, 35/(15-x)=140/(15+x). we are using (15-x) and (15+x) for the rate downstream and upstream respectively. Since the current of the river will speed the boat up as much as it will slow it down, the equality will work. when you solve the equation you will get x=9. since when the boat goes downstream it speeds up by x kph, its speed when its going downstream is 15kph+9kph..which is 24

Answer 3

The velocity of the boat going upstream is the still water speed MINUS the velocity of the water.

V_up = V_still - V_water

The velocity of the boat going down stream is the still water speed PLUS the velocity of the water.

V_down = V_still + V_water

From the other info we know:

t_up = 35/V_up
t_down = 140/V_down

we also know that:

t_up = t_down

35/V_up = 140/V_down

or

35*V_down = 140*V_up

35(15 + V_water) = 140*(15 - V_water)

you'll find:

V_water = 9kph

so V_up = 15 + 9 = 24

Answer 4

Write your equation. Let the river speed be x then the time to go upstream is 35/ (15 - x) and the time to go downstream is 140/(15+x)

Set these two functions equal and solve for x

35/(15-x) = 140/(15+x)

(15+x)/140 = (15-x)/35

15/140 + x/140 = 15/35 - x/35

x(1/35 + 1/140) = 15/35 - 15/140

x = (15/35 - 15/140) / (1/35 + 1/140)

x = 9kph

So the river is moving at 9kph

when the boat moves downstream it is traveling at 9 + 15 = 24kph with respect to the ground.

Answer 5

net velocity = boat velocity plus stream velocity
this is a (non-relativistic) vector equation
combine that with
v=d/t

upstream case:
35km/t = 15 kph - vstream
where vstream is the magnitude of the stream velocity,
and we subtract in this case since we're going upstream

downstream case:
140km/t = 15 kph + vstream

now we have two equations with two unknowns (t and vstream)
140 km/t = 15 kph + vstream
35 km/t = 15 kph - vstream
if we add these equations together to cancel vstream we get:
175 km/t = 30 kph
thus t = 175 km / 30 kph = 175/30 hr
the net downstream speed will be
140 km / t and we now know t, so
140 km / (175/30) hr = (2*2*2*3*5*5*7)/(5*5*7) kph =
24 kph

Answer 6

s = 15 kph

r = river speed

140 = (s+r)t ( river flow increases speed)

35 = (s -r )t (upriver travel is slowed by river speed)

Now 35 * 4 = 140

So 140 = 4(s-r)t

So: 4(s-r)t = (s+r)t

Factor out t

4(s-r) = s+r

4s - 4r = s+r
3s = 5r
s = speed = 15kph

45 = 5r

r = 9

So the boat travels 24 kph downstream and 6 kph upstream.

Answer 7

r = rate of current

(15 + r)(35) = (15 - r)(140)

15 + r = (15 - r) (4)

15 + r = 60 - 4r

5r = 45

r = 9

current = 9, speed = 15+9 = 24

Answer 8

r = rate of current

(15 + r)(35) = (15 - r)(140)

15 + r = (15 - r) (4)

15 + r = 60 - 4r

5r = 45

r = 9

current = 9, speed = 15+9 = 24

Answer 9

via fact that there are two times as many motorcycles as trucks, there are a hundred ninety motorcycles. This makes ninety 5 trucks, approximately 24 motorcycles and 1016 human beings. Divide the style of human beings extra to the style of motorcycles, it rather is 1040, with the aid of 4 and the respond is 285 autos.

Answer 10

15 kmph boat speed + stream = 140 km

15kmph boat speed - stream = 35 km
------------------------------------------------------ (add two equations)
30 kmph speed = 175 km

time = 5.83333

140 = rate (5.83333)
RATE = 24