SOLUTION: Jamie cycles 12 miles at a steady speed of x mph and then 25 miles at a steady speed of (x + 4) mph. Write down an expression, in terms of x, for the total time that Jamie ta

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Jamie cycles 12 miles at a steady speed of x mph and then 25 miles at a steady speed of (x + 4) mph. Write down an expression, in terms of x, for the total time that Jamie ta      Log On

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Question 808084: Jamie cycles 12 miles at a steady speed of x mph and then 25 miles at a steady speed of (x + 4) mph. Write down an expression, in terms of x, for the total time that Jamie takes.

The total time that Jamie takes is 2 hours. Form an equation in x and show that it simplifies to 2x^2-29x-48=0

Solve the equation 2x^2-29x-48=0 to find the speed x mph
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of distances according to r*t=d,
x%2A%28time1%29=12 and %28x%2B4%29%28time2%29=25
time1=12%2Fx and time2=25%2F%28x%2B4%29
Total Time is 12%2Fx%2B25%2F%28x%2B4%29

Now given that x=2 hours, 12%2Fx%2B25%2F%28x%2B4%29=2.
Does this match your equation?
%28x%28x%2B4%29%29%2812%2Fx%2B25%2F%28x%2B4%29%29=2x%28x%2B4%29
12x%2B48%2B25x=2x%5E2%2B8x
37x%2B48=2x%5E2%2B8x
2x%5E2%2B8x-37x-48=0
2x%5E2-29x-8x=0 Which is your equation as you found.

Is it factorable? Not sure, suspect not but maybe.
RESORT TO SOLUTION TO QUADRATIC FORMULA:

x=%2829%2Bsqrt%2829%5E2-4%2A2%2A%28-8%29%29%29%2F%282%2A2%29
x=%2829%2Bsqrt%2829%5E2%2B64%29%29%2F%282%2A2%29
x=%2829-sqrt%28777%29%29%2F%282%2A2%29

Look at sqrt%28777%29=sqrt%287%2A37%2A3%29, so just keep as the sqrt expression.
highlight%28x=%2829-sqrt%28777%29%29%2F4%29
Compute to highlight%28x=0.2813%29 miles per hour.

Jamie went for the first 12 miles at 0.28 miles per hour, or about 0.413 feet per second.