Question

Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves.
How many hours after the first car leaves will the two cars be 380 miles apart?


Enter an equation that can be used to solve this problem in the first box.

Solve for x and enter the number of hours in the second box.

Answer 1

Since the first car travels 55 miles per hour and starts an hour early, by 4:00 it is 55 miles away from the other car. Therefore, the equation is 55+a(some value)+b(another value)=380. If a car travels 55 miles per hour, that means that we add 55 for each hour and 55*x (if x is the number of hours) is the distance traveled. We have accounted for the first hour, so this is similar to saying that they start 55 miles away at 4:00 and go from there. For the other car, since it travels 75 miles per hour, its distance in hours is 75*x (the amount of time spent should be the same if we start at 4:00). Therefore, since they travel away from each other, our total distance is 55+55x+75x=380. Subtracting 55 from both sides (and combining like terms), we get 130x=325. Next, we divide both sides by 130 to get 2.5 hours, or 2 hours and 30 minutes

Answer 2

Solution-

Two cars leave the same location traveling in opposite directions.

The first car leaves at 3 p.m and has a speed of 55 mph

The second car leaves at 4 p.m and has a speed of 75 mph

Let x hours after the first car leaves, the two cars are 380 miles apart from each other.

$Speed =\frac{Distance}{Time}$

$\Rightarrow Distance=Speed\times Time$

In this x hours, distance covered by the first car,

$\Rightarrow Distance_1=Speed_1\times Time_1$

$\Rightarrow Distance_1=55\times x$

As the second car leaves at 4 p.m i.e 1 hour late as compared to the first car, so distance covered by the second car in (x-1) hours,

$\Rightarrow Distance_2=Speed_2\times Time_2$

$\Rightarrow Distance_2=75\times (x-1)$

According to the question,

$Distance_1+Distance_2=380$

$\Rightarrow 55\times x+75\times (x-1)=380$

$\Rightarrow 55x+75x-75=380$

$\Rightarrow 130x=455$

$\Rightarrow x=3.5$

∴ After 3.5 hours from 3 p.m i.e at 6.5 p.m the cars will have a distance of 380 miles.