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A boat goes upstream 30 miles and downstream 44 miles in 10 hours It also goes upstream 40 miles and downstream 55 miles in 13 hours Find the rates of the stream and of the boat?
Wiki User
∙ 13y ago
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:
- upstream speed = vb - vs mph
- downstream speed = vb + vs mph
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
Wiki User
∙ 13y ago
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If Tina swims 4 miles upstream at 1 mph and back downstream to the same point at 4 miles per hour what is her average speed?
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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,?
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.
If Tina swims 4 miles upstream at 1 mph and back downstream to the same point to the same point at 4 mph what is her average speed?
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A river has a current of 4 mph find the speed of simons boat in still water if it goes 40 miles downstream in the same time as 24 miles upstream?
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.
