Question

A cop is chasing after rob.Rob is running on the line y= 2x+5 at a speed of 2 units per second starting from the point (0,5). Cop starts running 't' seconds after Rob running at 3 units per second. Cop also starts at (0,5) and catches up to Rob at the point (17,39).Find the value of t.

Answer 1

Speed of a Rob = 2 Units/sec
Speed of Cop = 3 Units/sec

Total Distance covered = Distance between points (0,5) & (17,39)
= root[(17-0)^2 + (39-5)^2]
= root (289+1156)
= √1445 units

Time = ?
Time = Distance/Speed

Time required for the Rob to cover the distance ;
t'+t = √1445/2
t' = (√1445/2) -t ---------------(1)
Time required for the Cop to cover the same distance ;
t' = (√1445/3) ------------------(2)

Equating equation (1) & (2)

(√1445/2)-t = (√1445/3)
(√1445/2)-(√1445/3) = t
t = (3√1445 - 2√1444)/6

t = √1445/6 Seconds
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