The speed of the stream is 3mph and that of the boat is 8mph.
If vs is the speed of the stream, in mph and vb is the speed of the boat in mph, then:
Thus:
30/(vb-vs) + 44/(vb+vs) = 10
40/(vb-vs) + 55/(vb+vs) = 13
Multiplying both equations by (vb2-vs2) gives:
30(vb+vs) + 44(vb-vs) = 10(vb2-vs2)
40(vb+vs) + 55(vb-vs) = 13(vb2-vs2)
which rearrange to:
vb2-vs2 = (74vb - 14vs) / 10
vb2-vs2 = (95vb - 15vs) / 13
so, using the equality:
(74vb - 14vs) / 10 = (95vb - 15vs) / 13
12vb = 32vs
vb = 8/3 vs
thus using the first equation and the equality just worked out:
10((8/3 vs)2 - vs2) = 74(8/3 vs) - 14vs
vs10(64 / 9 - 1) = 74 x 8 / 3 - 14
vs10(55)/9 = (592 - 42)/3
vs550/9 = 550/3
vs = 3 mph
vb = 8/3 x 3 mph = 8 mph
Half an hour down stream one and a half hours upstream if the water is running at about 1 mile an hour.
2 Miles An Hour.
assume river velocity = X mph boat velocity = 20 mph time to go 6 miles downstream = T1 time to go 3 miles upstream = T2 distance = time * velocity downstream: 6 mi = T1 * (boat velocity + river velocity) upstream: 3 mi = T2 * (boat velocity - river velocity) 6 = T1 * ( 20 + X ) 3 = T2 * ( 20 - X ) T1 * ( 20 + X ) = 2 * ( T2 * ( 20 - X ) ) since T1 = T2 then 20 + X = 40 - 2X 3X = 20 X = 6.67 thus, river velocity is 6.67mph
A fisherman travels downstream at full speed to his favorite fishing spot. The stream is running at a rate of 5 miles per hour, and the trip takes 2 hours to get to the fishing hole. He is surprised, however, to find that the trip takes 6 hours at full speed to get back to the dock when he is finished. How fast will his fishing boat go? the boat is going 30 mph.
Let s = unknown speed in still water in units of miles per hour. The downstream speed will then be s + 4 and the upstream speed s - 4. In an equal time t in units of hours, t(s+4) = 40 and t(s-4) = 24. Multiplying out the parenthetical expressions yields ts + 4t = 40 and ts - 4t = 24. Subtracting the second of these equations from the first gives 8t = 16, or t = 2 hours. Therefore, ts +4t = 40, by substituting 2 for t becomes: 2s + 8 = 40, or 2s = 40 - 8 = 32, or s = 16 miles per hour.
Her average speed is 1.6 miles per hour. Average speed is total distance covered by total time taken to do it. She swims 4 miles upstream, and at 1 mph, it takes 4 hours. She comes back downstream at 4 mph and so she covers the 4 miles in 1 hour. Her total mileage is 8 miles. It takes 4 + 1 hours or 5 hours to cover it. The 8 miles divided by 5 hours is 1 3/5 miles per hour, or 1.6 mph for an average speed.
Half an hour down stream one and a half hours upstream if the water is running at about 1 mile an hour.
2 Miles An Hour.
Boats speed = 24 miles per hour.Current speed = 4 miles per hour.
assume river velocity = X mph boat velocity = 20 mph time to go 6 miles downstream = T1 time to go 3 miles upstream = T2 distance = time * velocity downstream: 6 mi = T1 * (boat velocity + river velocity) upstream: 3 mi = T2 * (boat velocity - river velocity) 6 = T1 * ( 20 + X ) 3 = T2 * ( 20 - X ) T1 * ( 20 + X ) = 2 * ( T2 * ( 20 - X ) ) since T1 = T2 then 20 + X = 40 - 2X 3X = 20 X = 6.67 thus, river velocity is 6.67mph
Speed upstream(S.u) = 20/5 => 4miles/hr Speed downstream(S.d) = 10/2 => 5miles/hr Speed of man in still water(speed of boat in still water)= 1/2 * (S.u + S.d) = 0.5 * (4 + 5) = 0.5 *9 = 4.5miles/hr The speed of man in still water is 4.5 miles/hr
The current is approximately 4 mph.
The gradient of the River Amazon is very low. It is 1,000 miles or 1,610 kilometers upstream, and 100 feet or 30 meters downstream.
A fisherman travels downstream at full speed to his favorite fishing spot. The stream is running at a rate of 5 miles per hour, and the trip takes 2 hours to get to the fishing hole. He is surprised, however, to find that the trip takes 6 hours at full speed to get back to the dock when he is finished. How fast will his fishing boat go? the boat is going 30 mph.
8 MPH
The speed of the jet stream is 110 mph (550 miles / 5 hours). In 5 hours, the plane covers 400 miles (80 mph x 5 hours). In 4 hours, the plane covers 320 miles (80 mph x 4 hours), but it actually covers 550 miles less due to the effect of the jet stream. So, the total distance traveled by the plane in 9 hours would be 720 miles (400 miles + 320 miles).
Let s = unknown speed in still water in units of miles per hour. The downstream speed will then be s + 4 and the upstream speed s - 4. In an equal time t in units of hours, t(s+4) = 40 and t(s-4) = 24. Multiplying out the parenthetical expressions yields ts + 4t = 40 and ts - 4t = 24. Subtracting the second of these equations from the first gives 8t = 16, or t = 2 hours. Therefore, ts +4t = 40, by substituting 2 for t becomes: 2s + 8 = 40, or 2s = 40 - 8 = 32, or s = 16 miles per hour.