Question

Six houses are located along the same road; the distances are shown. Where should the school bus stop to make the sum of distances from every house to the stop as small as possible?

PLEASE ANSWER ASAP!! I NEED IT TODAY!! I DON'T GET IT!! :(
The picture is attached.

Answer 1

Hey there :)

Now lets name each house

A B C D E F
500ft <-> 500ft <-> 500ft <-> 500ft <-> 500ft <-> 2000ft

Let's say the bus stops at A
= 0 ( from A ) + 500 ( from B ) + 500 + 500 ( from C ) + 500 + 500 + 500 ( from D ) + 500 + 500 + 500 + 500 ( from E ) + 500 + 500 + 500 + 500 + 2000 ( from F )
= 0 + 500 + 1000 + 1500 + 2000 + 4000
= 9000 ft

at B
= 500 ( from A ) + 0 ( from B ) + 500 ( from C ) + 500 + 500 ( from D ) + 500 + 500 + 500 ( from E ) + 500 + 500 + 500 + 2000 ( from F )
= 500 + 0 + 500 + 1000 + 1500 + 3500
= 7000 ft

at C
= 500 ( from A ) + 500 + 500 ( from B ) + 0 ( from C ) + 500 ( from D ) + 500 + 500 ( from E ) + 500 + 500 + 2000 ( from F )
= 500 + 1000 + 0 + 500 + 1000 + 3000
= 6000 ft

Do the same for D , E and F

at D
= 6000 ft

at E
= 7000 ft

at F
= 15000 ft

You will find that the bus should stop at either C or D to make the sum of distances from every house to the stop as small as possible.