Hi everybody! I hope your Fridays are going well I was hoping someone could help me understand a POD work and distance problem Greg covers in his work and distance practice video. I’ve watched the explanation and questions several times, but am still having a difficult time understanding how the solution was reached. The problem is:

A boy walking along a road at 3 kilometers per hour is overtaken by a truck traveling at 40 kilometers per hour. If the truck breaks down 1 kilometer beyond where it passes the boy, how many minutes after the breakdown does the boy reach the truck?

(A) 21 1/2

(B) 20

(C) 18 34/37

(D) 18 26/43

(E) 18 1/2

I know from Greg’s video the answer is E, and here is what I think I understand:

d= r x t

r Boy= 3kph

r train = 40kph

d= 1km

and then to make the rates into minutes, wouldn’t it be:

r Boy= 3/60

r train = 40/60

Here is where I get stuck:

if

d= r x t, shouldn’t the equation be something like

1= (3/60+40/60) x t

And then I realized, wait, the train has stopped and is no longer going 40/60 km per minute. So then I tried to find out how far the train went in 1 kilometers to subtract it from the boys rate.

1= 40/60xt

1/1 x 60/40 = time train took to travel = 60/40

so then 1 = (3/60)(60/40)

time it took boy = 180/2400

Which I know must be wrong, but I am VERY confused!! I’m still not even sure where Greg got the 1.5 from in his video. it must have been 60/40 but why would we do that instead of 40/60?? and how on earth does this problem work!! If anyone could help me understand it better I would be VERY grateful. At this point I feel like I’m a woman headed to remedial math class being overtaken by the train full of work and distance problems…