Question

D=RT Solve by setting up a system of linear equations with 2 variables and 2 unknowns. A Jeep and a BMW enter a highway that runs east-west at the same exit heading in opposite directions. The Jeep entered the highway 30 minutes before the BMW entered the highway, and traveled 7 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 306.5 miles apart. Find the speed of each car, if they were driven on cruise control

Answer 1

Explanation:

Alright, lets get started.

Lets suppose, the speed of jeep is j mph

Lets suppose, the speed of BMW is b mph

Jeep traveled 7 mph slower than the BMW, means

`b=j+7` equation (1)

The distance covered by BMW is 2 hrs =
`time*speed = 2b`

As jeep entered the highway 30minutes before, so jeep has advantage of 30 minutes or say half an hour.

Means traveling time for jeep is
`2+0.5 = 2.5`

The distance covered by Jeep in 2.5 hrs =
`2.5 j`

`2b+2.5j=306.5` equation (2)

Plugging the value of b from equation (1)

`2(j+7)+2.5j = 306.5`

`2j+14+2.5j=306.5`

`4.5j+14=306.5`

`4.5j=306.5-14=292.5`

`j=(292.5)/(4.5)=65`

Plugging the value of j in equation (1)

`b=j+7=65+7=72`

Hence the speed of BMW is 72 mph and speed of jeep is 65 mph. : Answer

Hope it will help :)