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?

1 Answer

Answer:

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

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

Explanation:

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"#