Question

Jim's speedboat can travel 22 miles upstream against a 3 mph current in the same amount of time it travels 24 miles downstream with a 3 mph current speed. Find the speed, in miles per hour, of the Jim's boat.

Answer 1

Explanation:

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=63 mph.

Answer 2

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

`\frac {22}{x-3}=\frac {24}{x+3}`

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