Math Problem?

Question

A rower travels upstream at 6km per hour and back to the starting place at 10km per hour. The total journey takes 48 minutes. How far upstream did the rower go?

Answer 1

let x be the distance travelled

Speed(s)=distance(d)/time(t)->t=d/s

Hence, you get:

x/6+x/10=48/60

(10x+6x)/60=48/60
x=3

Hence, total distance travelled=3km

Note: x/6=total time spent on upsteam, x/10=total time spent
on downsteam

Answer 2

Let T be the time upstream, in hours
Let 48/60 - T be the time downstream, in hours

Distance upstream = 6 km/hr * T
= 6T

Distance downstream = 10 km/hr * (48/60 - T)
= 8 - 10T

These two distance are the same so equate them:
6T = 8 - 10T
16T = 8
T = 0.5

So the rower took ½ hour upstream and 18 minutes downstream.

6 * 0.5 = 3 km

(Also 10 * 18/60 = 3 km)

The rower went 3 km upstream (and 3 km downstream obviously).

Answer 3

Distance = Speed X Time

Let x= distance upstream
t = time "
v = speed = 6km/h

for upstream journy
x = 6t
t = x/6...............(1)

Also x = distance to starting point
48/60 - t = Time note 60min = 1 hr
10km/h = speed

for return trip,
x = 10 (48/60 - t)...............(2)
sub. for t in eq. (2)
==> x = 10(48/60 - x/6)

==> x = 8 - 5x/3
5x/3 + x = 8
8x/3 = 8
==> x = 3 km

Answer 4

let us assume he travels distance x upstream and back distance x down stream.

time x speed= distance therefore distance/speed=time

this gives the equation

x/6 + x/10 = 48 mins since the speeds are in km/hr convert 48 mins into hrs that is 48/60

this gives 8x/30 = 48/60 this gives x=3 kilometers

he traveled 3 km upstream and then back 3 km down stream

Answer 5

3 km.

He is travelling upstream at 6 km/h, so it will take him half an hour, or 30 minutes to go upstream. Then travelling downstream, he is going at 10 km/h so it takes him 6 minutes per km. He spends 3 km* 6 min/km = 18 min on the downward leg.

The total journey takes 30 + 18 = 48 minutes.

Answer 6

The answer is 3 kilometers upstream.

To solve...

We'll use "x" to represent the distance upstream

Total time = distance*speed
^since we have two speeds over the same distance we will split that up...

6x + 10x

On the other side of the equation is the time

6x + 10x = 48
16x = 48
x = 3 km


Double checking......
3 km @ 6 km/hr = 0.5
3 km @ 10 km/hr = 0.3
Total = 0.8

Total * 60 to convert to minutes....
0.8 * 60 = 48 minutes (the given time)

Answer 7

distance [(6 + 10)/6*10] = 48/60
=> distance = 4/5*15/4 km = 3 km