Question

The average speed of a Greyhound bus from Lansing to Detroit is 105.5 km/h. On the return trip from Detroit to Lansing the average speed is 55.2 km/h on the same road due to heavy traffic. What is the average speed of the bus for the round trip?

Answer 1

We're going to use the equation d = rt

d = distance
r = rate (ie speed)
t = time

Answer 2

When it says "The average speed of a Greyhound bus from Lansing to Detroit is 105.5 km/h"

this means

d = rt

d = 105.5t

now solve for t to get

t = d/105.5

Answer 3

Then it says "On the return trip from Detroit to Lansing the average speed is 55.2 km/h on the same road due to heavy traffic."

so d is still the same (same distance), but the time is now different. So let's say the new time is x (instead of t

d = r*t

d = 55.2*x

solve for this new time x to get

x = d/55.2

Answer 4

with me so far?

Answer 5

yes! sorry I just saw this!

Answer 6

that's ok

Answer 7

The time it takes to go from Lansing to Detroit is d/105.5 hours

The time it takes to come back is d/55.2 hours

Answer 8

So the total time is just the sum of the two times, ie add them up


d/105.5+d/55.2

(d/105.5)*(55.2/55.2)+d/55.2

(55.2d)/5823.6+d/55.2

(55.2d)/5823.6+(d/55.2)*(105.5/105.5)

(55.2d)/5823.6+(105.5d)/5823.6

(55.2d+105.5d)/5823.6

160.7d/5823.6


The total time, in terms of the distance d, is 160.7d/5823.6 hours


This is a lot to take in, so go over it a few times and let me know when you're ready to move on.

Answer 9

Okay I got it

Answer 10

But where does the 55.2/55.2 come from?

Answer 11

Oh wait, okay I see

Answer 12

in order to add the fractions, the denominators had to be the same

so that's how you fix that

Answer 13

once you get it to (55.2d)/5823.6+(105.5d)/5823.6, you can add the fractions

Answer 14

so 160.7/5823.6?

Answer 15

the distance d is in there too

Answer 16

so the total time is 160.7d/5823.6

Answer 17

if d wasn't in there, then yeah, it would be 160.7/5823.6

Answer 18

Then do you solve for d?

Answer 19

so we know the total distance is d+d = 2d (basically double the distance to cover going there and back)

and the total time is 160.7d/5823.6

Answer 20

average speed = (total distance)/(total time)

Answer 21

if you divide the two, you'll find that the 'd' variables divide and cancel out

you'll be left with a number without variables

Answer 22

so I get .02759, but thats wrong when I put it in...did I do that wrong?

Answer 23

you should have

average speed = (2d)/(160.7d/5823.6)

simplify that

Answer 24

the answer you got is way too small

Answer 25

72.48?

Answer 26

I'm getting 72.47790916, but rounding that to 2 decimal places gives 72.48

Answer 27

Okay, thank you so much!

Answer 28

sure thing