Adam, Boris and Khan start from the same place and travel in the same direction at speeds of 15, 30 and 60 km per hour respectively. Boris starts two hours after Adam. If Boris and Khan overtake Adam at the same instant, how many hours after Adam did Khan start?a)4 hrsb)2 hrsc)3 hrsd)6 hrsCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Let us assume that Adam started running at 10 AM and Boris started at 12 noon.

So, in these two hours’ distance travelled by Adam is 30 km and the relative speed of Boris with respect to Adam is 15 km/hr.

So Boris will overtake Adam after =30/15 =2 hrs

So, Boris reaches there at 2 PM.

So, Khan also overtakes Adam at 2 PM.

Let us assume Khan takes t time to overtake Adam and the relative speed of Khan with respect to Adam is 45 km/hr and Adam ran for 4 hrs.

So, distance travelled by Adam is:

= time × speed

= 4 × 45 ……. (i)

While Khan's distance travelled is:

=t × 60 -------- (ii)

Since distance travelled by them is equal,

⇒ (i) = (ii)

⇒ 4 × 45 = t × 60

T = 3 hours

So, after 3 hrs, Khan will start running.

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