Question 1190217
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kph = kilometers per hour


60 kph = (60 km/1 hr)*(1 hr/60 min) = 1 km per min
80 kph = (80 km/1 hr)*(1 hr/60 min) = 4/3 km per min
Divide the kph value by 60 to convert to km per min.


In short,
60 kph = 1 km per min
80 kph = 4/3 km per min


x = amount of time, in minutes, the car has driven


The truck got a 20 minute head start, so it has traveled 20 minutes longer compared to x.
x+20 = amount of time, in minutes, the truck has driven



The truck drives at a speed of 1 km per min, so it travels a distance of 1*(x+20) = x+20 kilometers
Use the formula
Distance = rate*time


Meanwhile, the car travels (4/3)x kilometers


Summary table so far<table border = "1" cellpadding = "5"><tr><td>Vehicle</td><td>Distance (km)</td><td>Rate (km per min)</td><td>Time (minutes)</td></tr><tr><td>Car</td><td>(4/3)x</td><td>4/3</td><td>x</td></tr><tr><td>Truck</td><td>x+20</td><td>1</td><td>x+20</td></tr></table>The vehicles meet up when they have traveled the same distance.


Equate those two distance expressions and solve for x.
Car's distance = Truck's distance
(4/3)x = x+20
4x = 3(x+20)
4x = 3x+60
4x-3x = 60
x = 60
This is the amount of time, in minutes, needed for the car to meet up with the truck. Shortly afterward the car overtakes the truck.
Both vehicles travel 80 km when the two have met up.


Answer: <font color=red>1 hour</font>
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