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

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.