Help me on this math question.

[KEC029]

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This is from the sample question on ada.

QR #10

A person travels to work at an average speed of 40mph, and returns home at 60mph. Which of the following, in mph, is the average speed for the entire trip?

A. 45
B. 46
C. 48
D. 52
E. 54

Answer: C. 48

How is it C?😕

 

[1992Corolla]

I have no idea. I think I used to know though. Good luck😕

 

[reallylostnow]

u have to understand that the distance travelled is the same in both direction meaning he/she would be driving less time at 60 mph than 40 mph

quick way to think about it (at least for me)
assume the distance is 40 miles
so the "to work" travel time is one hour
to drive the same distance of 40 miles at 60 mph
would be 2/3 of an hour
so the total trip is 80 miles (forwards and back)
divide that by time (1 2/3 hours)
= 48 mph

hope that wasnt confusing
better than using random variables i think

 

[jjangmes]

This is how i approach tihs problem.
So the rate is going to be (total distance)/(total time)
Let's say total distance is D
distance to get to work = d1
total distance to get home = d2
d1 + d2 = D
d1=d2

For total time it took will be...since rate x time = distance, and
time = distance/rate... it will be d1/40 + d2/60. this will be our total time.

So D/(total time) = (d1 + d2)/ (d1/40 + d2/60)
2d/(d1/40 + d2/40) .... i wrote 2d, because d1=d2, so... total distance will be 2d

Since denominator is d1/40 + d2/40... you add them. which will be 5d/120
so.. which gives us... (2d)/(5d/120) ... which you can make it in to
((120)*(2d)/5d... which is 240d/5d.... cancel out d. and you get 240/5
which.. i think is 48?

 

[laundry]

you gotta do Total distance/total time (i know, makes no sense)

So i'd take a number representing the distance one way, easily divisible by 40 and 60 (120) and work with that.

120/40=3
120/60=2

(120*2)/5 = 48

cheers,

P.S. I was doing a Kaplan practice test and got a problem like that wrong (same mistake as you did),

 

[littlemissy]

you gotta do Total distance/total time (i know, makes no sense)

So i'd take a number representing the distance one way, easily divisible by 40 and 60 (120) and work with that.

120/40=3
120/60=2

(120*2)/5 = 48

cheers,

P.S. I was doing a Kaplan practice test and got a problem like that wrong (same mistake as you did),

exact way i do it..

u use d=rt

and get average speed by

d(total)/time(total)=avg speed(rate)

 

[KEC029]

Good people. Everything makes sense now!
Thank you 👍