A and B are two towns 360km apart. An express bus departs from A at 8a.m and maintains an average speed of 90km/h between A and B. Another bus starts from B also at 8a.m and moves towards A making four stops at four equally spaced points between B and A. Each stop is of duration 5 minutes and the average speed between any two stops is 60km/h. Calculate the distance between the two buses at 10p.m.


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Question Number 66865 by John Kaloki Musau last updated on 20/Aug/19

$A a n d B a r e t w o t o w n s 360 k m a p a r t .$ $A n e x p r e s s b u s d e p a r t s f r o m A a t$ $8 a . m a n d m a i n t a i n s a n a v e r a g e$ $s p e e d o f 90 k m / h b e t w e e n A a n d B .$ $A n o t h e r b u s s t a r t s f r o m B a l s o a t$ $8 a . m a n d m o v e s t o w a r d s A m a k i n g$ $f o u r s t o p s a t f o u r e q u a l l y s p a c e d$ $p o i n t s b e t w e e n B a n d A . E a c h s t o p$ $i s o f d u r a t i o n 5 m i n u t e s a n d t h e$ $a v e r a g e s p e e d b e t w e e n a n y t w o s t o p s$ $i s 60 k m / h . C a l c u l a t e t h e d i s t a n c e$ $b e t w e e n t h e t w o b u s e s a t 10 p . m .$
Commented by John Kaloki Musau last updated on 20/Aug/19

$T h e a n s w e r i s 65 k m .$ $p l e a s e d o i t .$
	Answered by John Kaloki Musau last updated on 20/Aug/19

	$d i s t a n c e t r a v e l l e d b y b u s 1$ $b e f o r e 10 a . m = 180 k m$ $d i s t a n c e t r a v e l l e d b y b u s 2$ $b e f o r e 10 a . m = 120 k m$ $120 k m o c c u s b t n d e p a r t u r e$ $p o i n t a n d f i r s t s t o p$ $1 s t s t o p = 5 m i n$ $10 a . m - 8 a . m - 5 m i n = 115 m i n$ $D = (\frac{115}{60} h r s \times 60 k m / h) k m = 115 k m$ $d i s t a n c e b t n b u s e s a t 10 a . m = {360 - (115 + 180)} k m$ $= 65 k m$
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