Linear System Motion Problem

Question

Shawn is training for a triathlon. He starts his workout by riding his nike for 1 hour and then runs for 1.5 hours. Shawn rides his bike 10 miles per hour faster than he runs. If he travelled a total of 27.5 miles, how fast did shawn bike?

Answer 1

The answer requested is expressed as a rate of speed (velocity).

Let's designate speed as 'r' (rate of motion)

Let's designate Time as  't'

Distance will be  'd'.  Overall total distance (27.5 mi) will be 'D'.

We have one hour at a rate of (run-speed * 10).

We have one and a half hours at run-speed.

These two components of "rate over a certain period of time", when combined, amount to a known distance.

Distance is rate multiplied by time.  [d=rt]

Rate is actually "distance per unit of time".  [r=d/t]

Total distance for our purposes will be 1.5 x r  plus  1 x 10r.

Broken down more deeply, we have   1.5 x (d/t)   +  1 x 10(d/t)

So . . .

 

D =  1.5 x (d/t) + 1 x 10(d/t)
D =  11.5 x (d/t)

27.5 = 11.5 x (d/t)

27.5 / 11.5 = 11.5 x (d/t)  /  11.5

2.4   =  d/t

2.4   =   r

24   =   10r

 

Shawn ran for 1.5 hours at 2.4 mi/hr, then rode for 1 hour at 24 mi/hr.

Shawn  covered 3.6 miles running and 24 miles biking - for a total of 27.6 miles

(rounding error due to using 2.4 instead of 2.391)