Question

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 5.2 mi/h

and biked at an average speed of 20.8 mi/h,

going a total of 14.4 miles. Seth ran at an average speed of 10.4 mi/h and biked at an average speed of 18.2 mi/h,

going a total of 18 miles. For how long do contestants run and for how long do they bike? Round to the nearest hundredth if necessary.


Contestants run__hour and bike___hour.

Answer 1

They ran for 0.923 hrs and biked for 0.46 hrs

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