Question

A boat has a speed of 15 mph in still water. it travels downstream from greentown to glenavon in g hours. it then goes back upstream from glenavon to cambria, which is 2 miles downstream from greentown, in g hours. find the rate of the current.

Answer 1

Answer

rate of current = (1/x) mph

Explanation
let the distance from Greentown to Glenavon be y miles and the rate of current be x mph.

y = (15+x)g
y = 15g+gx .........................................(1)

The distance from Glenavon to Cambria = (y-2)

y-2 =(15-x)g
y-2 = 15g-gx
y = 15g - gx + 2 ....................... (2)

equation equation (1) and (2)

15g + gx = 15g - gx + 2
2gx = 2

dividing by 2g both sides we get,

x = 1/2g mph

Answer 2

Word Problems: Travel and Distance

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a boat has a speed of 15 mph in still water. It travels downstream from Greentown, in three-fifths of an hour. It then goes back upstream from Glenavon to Cambria, which is two miles downstream from Greentown, in three fithts of an hour. Find the rate of the current.

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Let rate of the current be "c".

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Downstream DATA:

Time = (3/5) hr ; distance = x miles ; Rate = x/(3/5)= 5x/3 mph

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Upstream DATA:

Time = (3/5)hr ; distance= x-2 miles ; Rate = (x-2)/(3/5) = 5(x-2)/3 mph

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EQUATIONS:

Rate downstream: 15+c = 5x/3

Rate upstream : 15-c = 5(x-2)/3

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Add to get: 30 = [5x/3] + [5(x-2)/3]

Multiply thru by 3 to get:

5x + 5(x-2) = 90

10x=100

x = 10 miles

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Substitute into 15+c = 5x/3 to solve for "c":

15+c = 50/3

c = 50/3 - 45/3 = 5/3 mph

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Rate of the current is (5/3) mph

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Cheers,

Vasu J