Contestants in the Run-and-Bike-a-thon run for a specified length of time, then bike for a specified length of time. Jason ran at an average speed of 5.1 mi/h and biked at an average speed of 20.6 mi/h, going a total of 14.4 miles. Seth ran at an average speed of 10.2 mi/h and biked at an average speed of 18.8 mi/h, going a total of 17.4 miles. For how long do contestants run and for how long do they bike? Round to the nearest hundredth if necessary.
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Answer:
They ran for 0.923 hrs and biked for 0.46 hrs
Step-by-step explanation:
First thing to do is write down the inequality of the question
5.2x + 20.8y = 14.4
10.4x + 18.2y = 18
Multiplying the whole equation by 10, so as to eliminate the decimal places, we have.
52x + 208y = 144
104x + 182y = 180
Multiplying the first equation by 2, we have
104x + 416y = 288, next we solve it simultaneously with the second equation
104x + 416y = 288
104x + 182y = 180
Subtract 2 from 1, and we have..
416y - 182y = 288 - 180
234y = 108
y = 0.46
Now, we go back and substitute for y in the earlier equation, so that
52x + 208(0.46) = 144
52x + 95.68 = 144
52x = 144 - 95.68
52x = 48.32
x = 48.32/52
x = 0.929
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