A truck, P, travelling at 54km/h passes a point at 10:30 am while another truck, Q travelling at 90km/h passes through this same point 30 minutes later. At what time will truck Q overtake P?


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Question Number 201433 by necx122 last updated on 06/Dec/23

$A t r u c k, P, t r a v e l l i n g a t 54 k m / h p a s s e s$ $a p o i n t a t 10 : 30 a m w h i l e a n o t h e r t r u c k,$ $Q t r a v e l l i n g a t 90 k m / h p a s s e s t h r o u g h$ $t h i s s a m e p o i n t 30 m i n u t e s l a t e r . A t$ $w h a t t i m e w i l l t r u c k Q o v e r t a k e P ?$
	Answered by Rasheed.Sindhi last updated on 06/Dec/23

	$L e t P & Q m e e t a f t e r x h o u r s$ $o f 10 : 30$ $\begin{array}{cccc} P & Q \\ t i m e (i n h o u r s) & x & x - 1 / 2 \\ s p e e d (k m / h) & 54 & 90 \\ \underset{= s p e e d \times t i m e}{D i s t a n c e (k m)} & 54 x & 90 x - 45 \end{array}$ $54 x = 90 x - 45$ $36 x = 45 \Rightarrow x = 45 / 36 = 5 / 4 = 1 h o u r & 15 m i n u t e s$ $P a n d Q m e e t a t 11 : 45$
	Commented by necx122 last updated on 06/Dec/23
	This is indeed a great approach.
	Answered by mr W last updated on 06/Dec/23

	$a t 11 : 00 a m t r u c k P i s 0.5 \times 54 = 27$ $k m a h e a d o f t r u c k Q . t o o v e r t a k e P,$ $Q n e e d s \frac{27}{90 - 54} = 0.75 h = 45 m i n .$ $t h a t m e a n s a t 11 : 45 a m t r u c k Q$ $o v e r t a k e s t r u c k P .$
	Commented by necx122 last updated on 06/Dec/23
	As usual, your analytical skills are always baffling. Thank you for this approach.
	Answered by MathematicalUser2357 last updated on 06/Feb/24

	$‘ ‘ Q t r a v e l i n g a t 90 k m / h^{″}$ ${Y o u}^{'} r e q u o t i n g t h e q u e s t i o n .$
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