Shortcuts?
-
This post is deleted! -
[Originally posted in the Discussions]
Are there any shortcuts (e.g. formulas) that I can use to get the answer to these questions or is the solution only available through drawing on graph paper?
-
Yes, you can use the distance formula, which is:
distance = rate × time
or
d = r × t.
We want to know how many minutes apart the passenger trains are, so let's find out the distance that consecutive passenger trains are from each other. Here you can think of the rate equation as an expression of the relationship between distance, rate and time, and use it to convert between different quantities.
In order to find out the distance between consecutive passenger trains, we can just figure out all the pertinent distances in the problem. Starting from a point where we (the freight train) are just caught up to by passenger train number one, we know the distance it will have gone after one hour is:
d = (60 miles/hr) × (1 hr)
= 60 miles
The distance we will have gone after one hour is
d = (20 miles/hr) × (1 hr)
= 20 miles
The neat insight here is that at our location one hour later, passenger train number two has caught up to us, so it shares the same location as us.
So the distance between passenger train one and passenger train two is ( 60 miles - 20 miles ) = 40 miles!
Now we can figure out how many minutes apart the passenger trains leave by using the rate equation again:
d = r × t
40 miles = (60 miles/hr) × time
time = 40/60 hr = 40 minutes.
I hope this helps! Please don't hesitate to ask if you have any more questions!
Happy Learning,
The Daily Challenge Team
