In the time that it takes one car to travel 93 km, a second car travels 111 km. If the average speed of the second car is 12 km/h faster than the speed of the first car, what is the speed of each car?

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Answer 1 · 2018-08-06T18:21:06

$"Car 1" \ = \ "64 km/h"$

$"Car 2" \ = \ "74 km/h"$

The formula for speed is

$s=d/t$

For the first car, we know $d$ and plugging it into the formula gives us

$s_1=93/t$

We know the second car is $"12 km/h"$ faster and the distance is $"111 km"$ , so the formula in terms of the first car's speed would be

$s_1+12=111/t=s_2$

Now we can solve for $s_1$ in the second equation

$s_1=111/t-12$

Now we can set the two $s_1$ equal to each other and solve for $t$

$93/t=111/t-12$

$93=111-12t$

$12t=18$

$t=3/2 \ "hours"$

Now we can plug $t$ into the first car equation to solve for the speed of it

$s_1 = "93 km"/(3/2 \ "h") = "62 km/h"$

We know the second car is $"12 km/h"$ faster, so

$"62 km/h" \ + \ "12 km/h" = "74 km/h"$