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At 10:30 am car $A$ starts from point $A$ towards point $B$ at the speed of $65$ km/hr, at the same time another car left from point $B$ towards point $A$ at the speed of $70$ km/hr, the total distance between two points is $810$ km, at what time does these two cars meet ?

This is what I have tried,

$t_1 = \frac{810}{65} \,$ km/hr $= 12.46 \, $hr

$t_2 = \frac{810}{70} \,$ km/hr $= 11.57\,$ hr

$t_1-t_2 = 0.89 \,$ hr

$t_1-t_2 = 0.89\cdot 60 = 53.4 \,$ minutes

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but this couldn’t be the answer because how could these two cars could meet after $53.4$ minutes ?

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@Joe, when they start they are 810km apart; after 1 hour the person leaving from point A would have traveled 65km, so if the other person had not left from point B, then the distance between them would be 810-65=745km. But the other person also helps close the distance between them by traveling 70km in the 1st hour from point B towards A, so the distance between them is 810-(65+75)=810-135=675km. So they are effectively subtracting 135km worth of distance per hour from the original distance between them.

So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.

Hint: Think about how much closer the cars get each hour.

They are approaching each other at an effective speed of 135 km/hr…

**Hint:** The total distance between the two cars is initially $810~\text{km}$. Thus, in order to meet, the combined distance they travel is $810~\text{km}$. Since they are travelling toward each other, they get $65~\text{km} + 70~\text{km} = 135~\text{km}$ closer to each other each hour.

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