Calculating Relative Velocity for a Swimmer Training in a River

[percy_07]

A swimmer is training in a river. The current flows at 1.99 metres per second and the swimmer swims upstream a distance of 153 metres before swimming back to the starting point. If the total time for the swim is 192.0 seconds, what is the swimmer's speed relative to the water?

I've been stuck on this question for a while now just can't seem to get it out? Tried rearranging equations but still can't get to the answer of 2.94 m/s?

Any help would be greatly appreciated thankyou

 

[ehild]

Show your work, please.

ehild

 

[percy_07]

ok,

Current = 1.99 m/s
Total time = 192 s
Total distance traveled = (2x153) = 306 m

I've used the total time taken taken (192s) to be equal to the formula for the time taken upstream and downstream which looked like this.

192 = (153/ (x + (-1.99)) + (153/(x + 1.99)

rearranging and multiply out I've got down to

192 = 306x / x^2 - 3.9601

not sure how to solve for x any help??

 

[novop]

ok,

Current = 1.99 m/s
Total time = 192 s
Total distance traveled = (2x153) = 306 m

I've used the total time taken taken (192s) to be equal to the formula for the time taken upstream and downstream which looked like this.

192 = (153/ (x + (-1.99)) + (153/(x + 1.99)

So far so good.

rearranging and multiply out I've got down to

192 = 306x / x^2 - 3.9601

That's not right. Try again, you'll end up with a standard quadratic equation. Tip: multiply each fraction by the denominator of the other fraction to obtain a common denominator.

 

[percy_07]

That is what i had done cross multiplied to get that equation?

Is the denominator then added to get 2x^2-7.9202 I'm oblivious of where to go from hear very lost atm?

 

[percy_07]

i really need some clarification on this question it is doing my head in why i can't work it out, there is something that i am not taking into consideration but i don't know what it is please some help is required!

 

[ehild]

rearranging and multiply out I've got down to

192 = 306x / x^2 - 3.9601

Did you mean

$$192=\frac{306x}{x^2-3.9601}$$

? Then do not forget the parantheses: 192 = 306x / (x^2 - 3.9601).
Multiply the equation with the denominator, do the multiplication, arrange the equation so all terms are at one side, solve the quadratic equation.

ehild

 

[percy_07]

thanks for the help i resolved the question today what a relief