Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?

Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?

 2.30 p.m.

$\text{Let the distance between towns } P \text{ and } Q \text{ be } 275 \text{ km.}$

$\text{Speed of the first rider} = 25 \text{ km/hr}$
$\text{Speed of the second rider} = 20 \text{ km/hr}$

$\text{The first rider starts at } 8 \text{ a.m.}, \text{ and the second rider starts at } 9 \text{ a.m.}$
$\text{By the time the second rider starts, the first rider has traveled:}$

$ \text{Distance covered by first rider in 1 hour} = 25 \times 1 = 25 \text{ km} $

$\text{Remaining distance between them:}$

$ = 275 - 25 = 250 \text{ km} $

$\text{Relative speed when they move towards each other:}$

$ = 25 + 20 = 45 \text{ km/hr} $

$\text{Time taken to meet:}$

$ = \frac{250}{45} = \frac{50}{9} = 5.56 \text{ hours} $

$\text{Converting into hours and minutes:}$

$ 5.56 \text{ hours} = 5 \text{ hours } 33.6 \text{ minutes} $

$\text{The second rider started at } 9 \text{ a.m.}, \text{ so they will meet at:}$

$ 9 + 5 \text{ hours } 33.6 \text{ minutes} = 2:33 \text{ p.m.} $

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