A car travels along a straight line at a constant speed of 60.5 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 27.0 mi/h.
(a) What is the constant speed with which the car moved during the second distance d?

Question

A car travels along a straight line at a constant speed of 60.5 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 27.0 mi/h.
(a) What is the constant speed with which the car moved during the second distance d?

fifciol · Answer

average velocity= total distance/ total time=2d/total time

fifciol · Answer

total time is t1 + t2
t1=d/60.5
t2=d/v

substitute and solve for v

fifciol · Answer

$$27=\frac{ 2d }{ t_1+t_2 }=\frac{ 2d }{ \frac{ d }{ 60.5 }+\frac{ d }{ v } }=\frac{ 2d }{ \frac{ dv+60.5d }{ 60.5v } }=\frac{ 2d*60.5v }{d(v+60.5) }=\frac{ 121v }{ v+60.6 }$$

fifciol · Answer

27(v+60.5)=121v

fifciol · Answer

v=17.38 mi/h

anonymous · Answer

I absolutely can't thank you enough-- at this very moment i'm at a some starbucks, i've been beating my head against the wall over this problem. 

I've been through considerable amounts of math, but apparently coming into physics with a boastful attitude has proven to be of great handicap on my part. 

I thank you again!