8.8 Uniform Motion, Work, and Problem Solving

Question

Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?

Answer 1

r is the slower rate

t is the faster time

Tamara : 80 = t*(r+4)

Samantha : 80 = (t+1)*r

t*(r+4) = (t+1)*r

rt + 4t = rt + r

4t = r

80 = t*(4t+4)

20 = t*(t+1)

0 = t^2 + t - 20

0 = ( t + 5 )( t - 4 )

t-5 = 0 or t - 4 = 0

t +5=0 results in negative measures

t-4=0 --> t = 4

20 mph for 4 hours <--- Tamara

16 mph for 5 hours <--- Samantha