two cars leave same place at the same time. each car travels at a speed of 60kph. One travel in the direction 60° east of north. The other travel in the direction 45° east of south. How far apart are the two cars after 30 minutes
Answer:
11:51 am
The two cars are travelling in directions that are at right angle.
Let x and y be the distances travelled by the two cars in t hours.
Hence, x=50t and y=60t
Since the two directions are at right angle, Pythagoras theorem can used to find distance D between the two cars as follows:
D=
x
2
+y
2
We now find the time at which D=300 miles by solving
x
2
+y
2
=300
Square both sides and substitute x and y by 50t and 60t respectively to obtain the equation
(50t)
2
+(60t)
2
=300
2
Solve the above equations to obtain
t=3.84 hours (rounded to two decimal places) or 3 hours and 51 minutes (to the nearest minute)
The two cars will 300 miles apart at
8+3h51
′
=11:51 am
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