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 runhour and bike_hour.

Question

Mathematics

Newt

15 March, 21:49

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 runhour and bike_hour.

+3

Answers (1)

Know the Answer?

Danika Mckay · Answer 1

Let x be the running time and y the biking time.

5.2x+20.8y=14.4 and 10.4x+18.2y=18.

x+4y=14.4/5.2=36/13 so x=36/13-4y.

10.4 (36/13-4y) + 18.2y=18.

28.8-41.6y+18.2y=18, 10.8=23.4y so y=6/13 and x=36/13-24/13=12/13.

Contestants run 0.92 hour and bike 0.46 hour.