Carl is eating lunch at his favorite cafe when his friend Isaac calls and says he wants to meet him. Isaac is calling from a city 155 miles away, and wants to meet Carl somewhere between the two locations. Isaac says he will start driving right away, but Carl needs 31.0 min to finish his lunch before he can begin driving. Isaac plans to drive at 75.0 mph, and Carl plans to drive at 50.0 mph. Ignore acceleration and assume the highway forms a straight line. How long will Isaac be driving before he meets Carl?

Issac need 1.45 hours before he meets Carl

Explanation:

* Lets explain how to solve the problem

* The distance between Isaac and Carl is 155 miles

* Isaac says he will start driving right away

* Carl needs 31.0 min to finish his lunch before he can begin driving.

* Isaac plans to drive at 75.0 mph

* Carl plans to drive at 50.0 mph

* Ignore acceleration and assume the highway forms a straight line

Isaac will move immediately, but Carl needs 31 min to finish his lunch

So, assume that Isaac will spend t hours before meeting Carl

To find the Time of Carl to meet Issac change 31 minutes to hour

⇒ 1 hour = 60 minutes, then 31 minutes = 31/60 = 0.517 hr.

Carl will need t - 0.517 hour before meeting Isaac

The distance between Isaac and Carl is 155 miles

Distance = speed * time

Isaac drives at 75 mph

Carl drives at 50 mph

The distance that Isaac traveled before meeting Carl = 75t

The distance that Carl traveled before meeting Isaac = 50 (t - 0.517)

The sum of both distances is the total distance between their locations

⇒ 75t + 50 (t - 0.517) = 155

⇒ 75t + 50t - 25.83 = 155 ⇒ add like terms

⇒ 125t - 25.83 = 155 ⇒ add 25.83 to both sides

⇒ 125t = 180.83 ⇒ divide both sides by 125

⇒ t = 1.45

t represent the time that Isaac needs before meeting Carl

Issac need 1.45 hours before he meets Carl