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 5.8 mi/h and biked at an average speed of 20.2 mi/h, going a total of 14.6 miles. Seth ran at an average speed of 11.6 mi/h and biked at an average speed of 18.8 mi/h, going a total of 17 miles. For how long do contestants run and for how long do they bike? Round to the nearest hundredth if necessary.

Answer 1

Answer: The contestants run for 0.55 hour and they bike for 0.565 hour.

Explanation:

Since we have given that

Let the time taken for running be x and the time taken for biking be y

Average speed of running by Jason = 5.8 mi/h

Average speed of his bike = 20.2 mi/h

Total distance = 14.6 miles,

So, it becomes,

`5.8x+20.2y=14.6`--------------------(1)

Average speed of running by Seth = 11.6 mi/h

Average speed of his bike = 18.8 mi/hr

Total distance = 17 miles

`11.6x+18.8y=17`------------------(2)

So, From Eq(1), and (2), we get that

x=0.55 and y = 0.565

Hence, the contestants run for 0.55 hour and they bike for 0.565 hour.