SOLUTION: Solve using rational expressions and a distance-speed-time chart: Bob and Sam are long distance swimmers and are competing in a 2km swimming competition. Throughout the season,

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve using rational expressions and a distance-speed-time chart: Bob and Sam are long distance swimmers and are competing in a 2km swimming competition. Throughout the season,       Log On


   

Question 1171660: Solve using rational expressions and a distance-speed-time chart:
Bob and Sam are long distance swimmers and are competing in a 2km swimming competition. Throughout the season, Bob has been 0.7km/h faster than Sam, and Sam finishes the race 15 minutes after Bob. Determine the speed at which each of them swim, round to 1 decimal place.
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the Bob' speed, in kilometers per hour.

Then the Sam' speed is (x-0.7) km/h.


Bob' swimming time is  2%2Fx  hours.

Sam' swimming time is  2%2F%28x-0.7%29 hours.


The difference of swimming times is  15 minutes = 1%2F4 of an hour.


It gives THIS "time" equation


    2%2F%28x-0.7%29 - 2%2Fx = 1%2F4.



To solve it, multiply both sides by 4x*(x-0.7).  You will get


    8x - 8*(x-0.7) = x*(x-0.7)

               5.6 = x^2 - 0.7x

    x^2 - 0.7x - 5.6 = 0

    x%5B1%2C2%5D = %280.7+%2B-+sqrt%280.7%5E2+%2B+4%2A5.6%29%29%2F2 = %280.7+%2B-+sqrt%2822.89%29%29%2F2 = %280.7+%2B-+4.78%29%2F2.


Of the two roots, only positive value does work  x = %280.7+%2B+4.78%29%2F2 = 2.74.


So, the ANSWER is: the Bob' speed is  2.7 km/h; the Sam' speed is  2.7 - 0.7 = 2.0 km/h  (both values are rounded).

Solved.


============

I hate using distance-speed-time charts.

Teaching this way is the same as teaching small healthy baby to walk using crutches.


Then the student thinks about this table, but not about the problem.

My criterion is: if the student needs/uses such table, it means that he (or she) does not know the method
and does not know the right approach to the problem.


Therefore, I teach via the LOGIC of the problem, hoping that in this way it will go through the student's mind.


It is how my teachers taught me in my secondary school.
They were masters of teaching (!)