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Jim's speedboat can travel 21 miles upstream against a 3 mph current in the same amount of time it travels 23 miles downstream with a 3 mph current speed. Find the speed, in miles per hour, of the Jim's boat.

User Divek John
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1 Answer

2 votes

Answer:

69 mph

Explanation

Let the speed of boat be x hence speed downstream is x+3 but speed upstream will be x-3

Speed is distance per unit time and time is same hence

24(x-3)=22(x+3)

24x-72=22x+66

2x=138

X=138/2=69

Therefore, the speed of boat is 69 miles per hour or

The boat in the problem travels different distances at different rates, but in the same amount of time for each trip. Distance is rate times time, d=r⋅t, which, solving for t, becomes

t=dr.

The trip against the current has rate r=s−3, so the time it takes to complete the trip is

t=20s−3.

The time it takes to complete the trip with the current is

t=22s+3.

The time to complete each trip is the same, so set the fractions equal to each other.

20s−3=22s+3

Multiply each side by (s−3)(s+3).

20(s−3)(s+3)(s−3)=22(s−3)(s+3)(s+3)

Simplify.

20(s+3)=22(s−3)

Distribute coefficients.

20s+60=22s−66

Combine like terms.

2s=126

Divide each side by 2 to find the solution,

s=69 mph.

Sorry if im wrong

User Dheeraj Malik
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