+479 A boat can cover 12 km up the stream and 75% of that distance down the stream in 6 hours. Find the speed of the boat in still water if the speed of the stream is 41 2/3 meters per minute.
+2094 Not entirely sure about this one... Try setting an equation. Let x be the speed of the boat.
(x+41 2/3) + 3/4(41 2/3-x)= 3/4(12) + 12 = 21
+129852 Convert speed in m/min to km /h
41 +2/3 m / min x 60 min = 2500 m/ hr = 2.5 km / hr
Let R be the rate of the boat in still water
[75% of 12 = 9]
And note that D /R = Total time
Rate downstream = R + 2.5 Rate upstream = R - 2.5
Distance downstream / Rate Downstream + Distance upstream/ Rate upstream = Total time
12 / [ R + 2.5] + 9 / [ R - 2.5 ] = 6
(12 [ R-2.5] + 9 [ R + 2.5] ) / [ (R+ 2.5 ) (R -2.5)] = 6
[ 12 R - 30 + 9R + 22.5]/ (R^2 - 6.25) = 6
21R - 7.5 = 6 [ R^2 - 6.25 ]
21R - 7.5 = 6R^2 - 37.5 rearrange as
6R^2 - 21R - 30 = 0 divide through by 3
2R^2 - 7R - 10 = 0
Using the quadratic formula
R = ( 7 + sqrt [ ( 7^2 - (4)*(2) *( -10)] ) / ( 2 * 2) = ( 7 + sqrt ( 129)) / 4 ≈ 4.6 km/h
+2094 Darn, I think I made a mistake! Nice job, CPhill and for the op check his answer instead :)
Rate * time = distance 41 2/3 meters/min = 2.5 km/hr
time = distance/r
6= 12/(r-2.5) + 9 /(r+2.5)
6 (r-2.5)(r+2.5) =12 (r + 2.5) + 9 ( r-2.5)
6 (r^2 -6.25) =
6 r^2 -37.5 = 12 r + 30 + 9r - 22.5
6r^2 -21r - 45 =0
r= 5 km/hr (via quadratic equation)
CHECK: 12 km / (5-2.5)km/hr + 9 km / (5+2.5)km/hr = 6 hours CHECK !
