MathDB

Two men,

A

and

B

, set out from town

M

to town

N

, which is

15

km away. Their walking speed is

6

km/hr. They also have a bicycle which they can ride at

15

km/hr. Both

A

and

B

start simultaneously,

A

walking and

B

riding a bicycle until

B

meets a pedestrian girl,

C

, going from

N

M

. Then

B

lends his bicycle to

C

and proceeds on foot;

C

rides the bicycle until she meets

A

and gives

A

the bicycle which

A

rides until he reaches

N

. The speed of

C

is the same as that of

A

and

B

. The time spent by

A

and

B

on their trip is measured from the moment they started from

M

until the arrival of the last of them at

N

.
a) When should the girl

C

leave

N

for

A

and

B

to arrive simultaneously in

N

? b) When should

C

leave

N

to minimize this time?

Problem Statement