Work and Distance POD-don't understand explanation

GRE Quant Problem Solving
1

Hi everybody! I hope your Fridays are going well :slight_smile: 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…

2

You are correct till here
Now instead of quickly plugging value into the equation, try to understand the problem:
It says the truck breakdowns 1 km after crossing the boy.
Time elapsed b/w overtaking and breakdown = t = d/r(truck) = 1/(40/60) = 60/40 = 1.5 minutes
Distance travelled by the boy in that time = d = r(boy) x t = 3/60 x 1.5 = 0.075 km
Distance left to be travellevd by the boy =
Dist b/w current position and breakdown = DIst b/w overtaking and breakdown point - Dist b/w overtaking and current position =
1 - 0.075 = 0.925 km
Time that will be take by the boy to reach the breakdown point = t = d/r = 0.925/(3/60) = 18.5

Option (e)
Hope this makes sense

3

Thank you so much Vidishas! I didn’t take into account that the boy would still be traveling during the time the train would, and didn’t understand that the key to solving the problem, like you pointed out, is finding the difference between that one kilometer MINUS the amount the boy traveled, and then converting that to minutes. I’m very grateful, this makes a lot more sense that what I had originally thought! :smiley: