Respuesta :
Car takes 23.076 minute to pass the truck
Solution:
A truck enters a highway driving 60 mph
A car enters the highway at the same place 5 minutes later and drives 73mph in the same direction
Let us consider,
Truck speed = 60 mph ( given )
Time for the truck = T hour
The distance is given as:
[tex]distance = speed \times time[/tex]
Therefore,
[tex]distance = 60 \times T\\\\Distance = 60T ------- eqn 1[/tex]
Let us consider
Car speed = 73 mph ( given )
car time = T - 5minutes
We know that,
1 hour = 60 minutes
Therefore,
[tex]Car\ time = T - \frac{5}{60}\ hour\\\\Car\ time = T - \frac{1}{12}\ hour[/tex]
Distance of car:
[tex]Distance = 73 \times (T - \frac{1}{12}) ------ eqn 2[/tex]
The two distances are equal:
[tex]60T = 73(T - \frac{1}{12})\\\\60T = 73T - \frac{73}{12}\\\\60T = 73T - 6.0833\\\\73T - 60T = 6.0833\\\\13T = 6.0833\\\\Divide\ both\ sides\ by\ 13\\\\T = 0.4679[/tex]
How long will it take the car to pass the truck?
[tex]Car\ time = T - \frac{1}{12}\ hour\\\\Car\ time = 0.4679 - 0.0833\\\\Car\ time = 0.3846\ hour\\\\Car\ time = 23.076\ minute[/tex]
Thus car takes 23.076 minute to pass the truck
