Question

1 ) During his morning commute to work in rush hour traffic, Justin's average speed was 30 mi/h. During his afternoon commute back home along the same route, his average speed was 60 mi/h. What was his average speed for the entire round trip?
15 points, answer correctly, please!

Answer 1

Answer:45 mi/h

Step-by-step explanation:

Recall: Speed = distance / time

Let the time taken for the morning journey be $t_{1}$ and the time taken for the afternoon journey be $t_{1}$ ,and the distance covered be d

that means for the first journey,

30 = $\frac{d}{t_{1}}$

d = 30 $t_{1}$

Also for the afternoon journey,

d = 60 $t_{2}$

Equating the two , since the same distance is being covered , we have

30 $t_{1}$ = 60 $t_{2}$

that is

$t_{1}$ = $\frac{60t_{2}}{30}$

$t_{1}$ = 2 $t_{2}$

Also ,

total distance covered = 30 $t_{1}$ + 60 $t_{2}$

Average speed = total distance / total time

 = 30 $t_{1}$ + 60 $t_{2}$ / $t_{1}$ +$t_{2}$

  Recall that   $t_{1}$ = 2 $t_{2}$ , substitute this  into the formula for average speed , then we have

Average speed = 30(2$t_{2}$) +60 $t_{2}$ / 3$t_{2}$

Average speed = 120$t_{2}$ / 3$t_{2}$

Therefore :

Average speed = 40 mi/hr