Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The two cars start from the same point in opposite directions at 40 and 50 mph. The speed at which the two cars are moving away from each other is given by 40 + 50 = 90 mph.

They are 450 miles apart from each other after 450/90 = 5 hours.

As the cars had started at 5 AM, they will be 450 miles apart at 5 + 5 = 10 AM

The required time when the 2 cars will be 450 miles apart is 10 AM.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let us call the cars A and B.

Car A travels at S(A) = 40 mph

Car B travels at S(B) = 50 mph

We need to know the time T such that the distance between the cars is 450 m.

1.Let us assume that the distance car A travels is DA

and the distance that car B travels is DB

==> D = DA + DB = 450..........(1)

Now let us calculate the time.

T = D/S

==> T = DA/ 40

==> T= DB/50

==> DA/40 = DB/50

==> DA/4 = DB/ 5

But DA + DB = 450

==> (450-DB) /4 = DB/5

==> (450-DB)*5 = 4DB

==> 2250 - 5DB = 4DB

==> 9DB = 2250

==> DB = 250 miles

==> T = 250/50 = 5 hours,

Then the cars will be 450 miles apart after 5 hours.

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