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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
0

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
+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.

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

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

$$\large s=250km$$

$$The \ cities \ X \ and \ Y \ are \ 250\ km \ apart.$$ !

May 23, 2017
edited by asinus  May 23, 2017
#3
+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   May 23, 2017