i need help with a distance rate and time application word problem

Question

(applications of rational equations and proportions)

'An athlete in training rides his bike 20mi and then immediately follows with 10 mile run. The total workout takes him 2.5hr. he also knows that he bikes twice as fast as he runs. Determine his biking speed and his running speed.

Answer 1

Time = distance/rate.  Let B=biking speed and R=running speed.

 

Total time = 20/B + 10/R

B = 2R

 

2.5 hr = 20 mi/2R + 10 mi/R

2.5 hr = 10 mi/R + 10 mi/R

2.5 hr = 20 mi/R

R(2.5 hr) = 20 mi

R = 20 mi/2.5 hr

R = 8 mi/hr

B = 2(8 mi/hr) = 16 mi/hr

 

So his biking speed is 16mph and his running speed is 8mph.

Answer 2

Let R = running speed and B = biking speed and note that B = 2R

 

Time biking = 20/B and time running = 10/R

 

20/B + 10/R = 5/2

 

Substitute

 

20/2R + 10/R = 5/2

 

Multiply by R to get: 10 + 10 = 5R/2 =>5R = 40 and R=8

 

Then B = 16