Sarthak completed a marathon in 4 hours and 35 minutes.

Sarthak completed a marathon in 4 hours and 35 minutes. The marathon consisted of a 10 km run followed by 20 km cycle ride and the remaining distance again a run. He ran the first stage at 6 km/hr and then cycled at 16 km/hr. How much distance did Sarthak cover in total, if his speed in the last run was just half that of his first run?

Let the total distance be x km.

Time =	Distance
	Speed

According to the question,

10	+	20	+	x − 30	= 4	35
6	+	16	+	3	= 4	60

= 4	7
	12

⇒	5	+	5	+	x	− 10 =	55
	3		4		3		12

⇒	x	+	5	+	5	− 10 =	55
	3		3		4		12

⇒	x	+		20 + 15 − 120		=	55
	3			12			12

⇒	x	−	85	=	55
	3		12		12

⇒	x	=	85	+	55	=	140
	3		12		12		12

⇒ x =	140	× 3 = 35 km.
	12