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A car travelling from Town X to Town Y passed a van halfway.The van was travelling in the opposite direction at a uniform speed of 40 km/h.2.5 hours later,the car reached Town Y and the van was still 25 km from Town X.Find the distance between Town X and Town Y.

 May 23, 2017
 #1
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A car travelling from Town X to Town Y passed a van halfway.The van was travelling in the opposite direction at a uniform speed of 40 km/h.2.5 hours later,the car reached Town Y and the van was still 25 km from Town X.Find the distance between Town X and Town Y.

Average speed =Distance /Time
Let the distance between between the 2 towns =D
Let the average speed of the car =S. But we have:
(1/2D) / 2.5 =S. And we also have:
40 =[(1/2D) - 25] / 2.5, Solve for D, S
D = 250 Km - distance between towns X and Y
S =50 Km/h - average speed of the car

 May 23, 2017
 #2
avatar+8079 
+1

A car travelling from Town X to Town Y passed a van halfway.The van was travelling in the opposite direction at a uniform speed of 40 km/h.2.5 hours later,the car reached Town Y and the van was still 25 km from Town X.Find the distance between Town X and Town Y.

 

\(\frac{s}{2}=2.5h\cdot40\frac{km}{h}+25km\)

 

 

\(s=2(2.5h\cdot40\frac{km}{h}+25km)=200km+50km\)

 

\(\large s=250km\)

 

\(The \ cities \ X \ and \ Y \ are \ 250\ km \ apart.\)

 

laugh  !

 May 23, 2017
edited by asinus  May 23, 2017
 #3
avatar+98196 
+1

 

 

A car travelling from Town X to Town Y passed a van halfway.The van was travelling in the opposite direction at a uniform speed of 40 km/h.2.5 hours later,the car reached Town Y and the van was still 25 km from Town X.Find the distance between Town X and Town Y.

 

Call the car's rate, R

 

And the rate it travels times the time it travels  =  R * 2.5     =  the halway distance between the towns = (1)

And the rate the van travels (40 km/hr ) times 2.5 hrs  + 25 km  =  (1)

 

So....setting these equal, we have

 

R * 2.5    =   40* ( 2.5) + 25   simplify

 

2.5 R   =  100 + 25

 

2.5R   = 125   divide both sides by 2.5

 

R  = 50 km/hr

 

Then....this the rate of the car........so......the  distance between the towns  =  2* (2.5)* 50 =  250 km

 

 

 

 cool cool cool

 May 23, 2017

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