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 135 miles away, and wants to meet Carl somewhere between the two locations. Isaac says he will start driving right away, but Carl needs 27.0 min to finish his lunch before he can begin driving. Isaac plans to drive at 70.0 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?

Isaac will take 1.3125 hours before he meets Carl

Explanation:

Lets explain how to solve the problem

The distance between Carl and Isaac is 135 miles

Issac will start driving first

Carl will start driving 27 minutes after Isaac

Isaac will drive at 70 miles per hour

Carl will drive at 50 miles per hour

We will ignore the acceleration and assume the highway forms a

straight line

Lets consider that Isaac takes t hours and travel distance d miles

before he meets Carl

Carl start driving after Isaac by 27 minute, lets change the minutes to

hour because the speed is miles per hour

⇒ 1 hr = 60 min

⇒ 27 minutes = 27/60 = 0.45 hour

Isaac will take t hour before he meets Carl

Then Carl will take t - 0.45 hour before he meets Isaac

Isaac will travel d miles before he meets Carl

Then Carl will travel s miles before he meets Isaac

The distance between Carl and Isaac is 135 miles

Then d + s = 135 ⇒ (1)

Isaac will travel at 70 mi/h

Carl will travel at 50 mi/h

Distance = speed * time

Then d = 70t and s = 50 (t - 0.45)

Substitute the value of d and s in equation (1)

70t + 50 (t - 0.45) = 135

70t + 50t - 22.5 = 135

120t - 22.5 = 135 (add both sides by 22.5

120t = 157.5 (divide both sides by 120)

t = 1.3125

t represents the time of Isaac before he meets Carl

Isaac will take 1.3125 hours before he meets Carl