A car and a train leave the same point at the same moment. The car travels at #30# #kmh^-1# and the train at #40# #kmh^-1# at right angles to the direction the car travels. How far apart are the two vehicles after #6# minutes?

1 Answer
David G.
Jul 25, 2017

The car travels #3# #km# and the train travels #4# #km# at right angles to it, so they end up #5# #km# apart.

Explanation:

We could convert into #ms^-1#, but let's work in kilometres per minute instead.

First step is to draw a diagram (but I will leave that for you to do). We have to assume that they start at exactly the same point.

If the car is travelling #30# #km# each hour then it is traveling #30/60=0.5# #km# each minute (because there are 60 minutes in an hour). In #6# min it will travel #6xx0.5=3# #km# due north.

Similarly, the train is travelling #40/60=2/3# #km# per minute, so in #6# min it will travel #6xx2/3=4# #km# due east.

To find the distance they are apart we can use Pythagoras' theorem, since their paths form a right-angled triangle. I'll the the calculation in a minute, but I happen to remember that a right-angled triangle with sides 3 and 4 units long has a hypotenuse 5 units long.

#a^2=b^2+c^2=3^2+4^2=9+16=25#

#a=sqrt(25)=5#

Sure enough, the car and train are #5# #km# apart.

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